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In this work, we theoretically demonstrate that a strong enhancement of the Magnetocaloric Effect is achieved in geometrically frustrated cluster spin-glass systems just above the freezing temperature. We consider a network of clusters interacting randomly which have triangular structure composed of Ising spins interacting antiferromagnetically. The intercluster disorder problem is treated using a cluster spin glass mean-field theory, which allows exact solution of the disordered problem. The intracluster part can be solved using exact enumeration. The coupling between the inter and intracluster problem incorporates the interplay between effects coming from geometric frustration and disorder. As a result, it is shown that there is the onset of cluster spin glass phase even with very weak disorder. Remarkably, it is exactly within a range of very weak disorder and small magnetic field that is observed the strongest isothermal release of entropy., Comment: 10 pages, 7 figures. Provisionally accepted in Journal of Physics: Condensed Matter

Quenched disorder effects on frustrated systems are explored by considering random fluctuations on the antiferromagnetic (AF) interactions between spins on the checkerboard lattice. The replica framework is adopted within a cluster mean-field approach, resulting in an effective single-cluster model. This effective model is treated within a one-step replica symmetry breaking (RSB) approach with exact evaluations for all intracluster interactions. Competing interactions are introduced by tuning the ratio $J_2/J_1$ (where $J_1$ and $J_2$ are first-neighbour and second-neighbor interactions, respectively), which can lead to a highly frustrated scenario when $J_2/J_1\rightarrow 1$, where a phase transition between AF orders takes place in the absence of disorder. In particular, the AF order appears at lower values of $J_2/J_1$, with the Neel temperature decreasing as the frustration increases. However, quenched disorder changes this description, introducing a RSB spin glass phase for strong enough disorder intensity $J$. In fact, for low levels of disorder, a RSB solution with staggered magnetization (mixed phase) emerges from the maximum frustration region. It suggests that, in the presence of weak quenched disorder, systems with competing interactions are prone to present a glassy behavior instead of conventional orders., Comment: 7 pages, 4 figures

Recent results for the Ising model with first ($J_1$) and second ($J_2$) neighbour interactions on the body-centered cubic (bcc) lattice suggest that this model can host signatures of strong frustration, including Schottky anomalies and residual entropy, as well as, a spin-liquid-like phase [E. Jur\v{c}i\v{s}inov\'a and M. Jur\v{c}i\v{s}in, Phys. Rev. B, 101 214443 (2020)]. Motivated by these findings, we investigate phase transitions and thermodynamics of this model using a cluster mean-field approach. In this lattice, tuning $g=J_2/J_1$ leads to a ground-state transition between antiferromagnetic (AF) and superantiferromagnetic (SAF) phases at the frustration maximum $g=2/3$. Although the ordering temperature is reduced as $g \to 2/3$, our findings suggest the absence of any Schottky anomaly and residual entropy, in good agreement with Monte Carlo simulations. We also find a direct transition between AF and SAF phases, ruling out the presence of the spin-liquid-like state. Furthermore, the cluster mean-field outcomes support a scenario with only continuous phase transitions between the paramagnetic state and the low-temperature long-range orders. Therefore, our results indicate the absence of strong frustration effects in the thermodynamics and in the nature of phase transitions, which can be ascribed to the higher dimensionality of the bcc lattice., Comment: 6 pages, 6 figures

In this paper, we focus on the use of Low-Eart Orbit (LEO) satellites providing the Narrowband Internet of Things (NB-IoT) connectivity to the on-ground user equipment (UEs). Conventional resource allocation algorithms for the NBIoT systems are particularly designed for terrestrial infrastructures, where devices are under the coverage of a specific base station and the whole system varies very slowly in time. The existing methods in the literature cannot be applied over LEO satellite-based NB-IoT systems for several reasons. First, with the movement of the LEO satellite, the corresponding channel parameters for each user will quickly change over time. Delaying the scheduling of a certain user would result in a resource allocation based on outdated parameters. Second, the differential Doppler shift, which is a typical impairment in communications over LEO, directly depends on the relative distance among users. Scheduling at the same radio frame users that overcome a certain distance would violate the differential Doppler limit supported by the NB-IoT standard. Third, the propagation delay over a LEO satellite channel is around 4-16 times higher compared to a terrestrial system, imposing the need for message exchange minimization between the users and the base station. In this work, we propose a novel uplink resource allocation strategy that jointly incorporates the new design considerations previously mentioned together with the distinct channel conditions, satellite coverage times and data demands of various users on Earth. The novel methodology proposed in this paper can act as a framework for future works in the field., Comment: Tis work has been submitted to the IEEE IoT Journal for possible publication

We study magnetic properties of spin glass SG systems under a random field (RF), beased on the suggestion that RFs can be induced by a weak transverse field in the compound LiHo$_x$Y$_{1-x}$F$_4$. We consider a cluster spin model that allows long-range disordered interactions among clusters and short-range interactions inside the clusters, besides a local RF for each spin following a Gaussian distribution with standard deviation $\Delta$. We adopt the one-step replica symmetry breaking (RSB) approach to get an exactly solvable single-cluster problem. We discuss the behavior of order parameters, specific heat $C_{m}$, nonlinear susceptibility $\chi_3$ and phase diagrams for different disorder configurations. In the absence of RF, the $\chi_3$ exhibits a divergence at $T_f$, while the $C_{m}$ shows a broad maximum at a temperature $T^{**}$ around 30$\%$ above $T_f$, as expected for conventional SG systems. The presence of RF changes this scenario. The $C_{m}$ still shows the maximum at $T^{**}$ that is weakly dependent on $\Delta$. However, the $T_f$ is displaced to lower temperatures, enhancing considerable the ration $T^{**}/T_f$. Furthermore, the divergence in $\chi_3$ is replaced by a rounded maximum at a temperature $T^{*}$, which becomes increasingly higher than $T_f$ as $\Delta$ enhances. As a consequence, the paramagnetic phase is unfolded in three regions: (i) a conventional paramagnetism ($T>T^{**}$; (ii) a region with formation of short-range order with frozen spins ($T^{*}

We investigate the role of a transverse field on the Ising square antiferromagnet with first-($J_1$) and second-($J_2$) neighbor interactions. Using a cluster mean-field approach, we provide a telltale characterization of the frustration effects on the phase boundaries and entropy accumulation process emerging from the interplay between quantum and thermal fluctuations. We found that the paramagnetic (PM) and antiferromagnetic phases are separated by continuous phase transitions. On the other hand, continuous and discontinuous phase transitions, as well as tricriticality, are observed in the phase boundaries between PM and superantiferromagnetic phases. A rich scenario arises when a discontinuous phase transition occurs in the classical limit while quantum fluctuations recover criticality. We also find that the entropy accumulation process predicted to occur at temperatures close to the quantum critical point can be enhanced by frustration. Our results provide a description for the phase boundaries and entropy behavior that can help to identify the ratio $J_2/J_1$ in possible experimental realizations of the quantum $J_1$-$J_2$ Ising antiferromagnet., Comment: are welcome

The interplay between geometric frustration (GF) and bond disorder is studied in the Ising kagome lattice within a cluster approach. The model considers antiferromagnetic (AF) short-range couplings and long-range intercluster disordered interactions. The replica formalism is used to obtain an effective single cluster model from where the thermodynamics is analyzed by exact diagonalization. We found that the presence of GF can introduce cluster freezing at very low levels of disorder. The system exhibits an entropy plateau followed by a large entropy drop close to the freezing temperature. In this scenario, a spin-liquid (SL) behavior prevents conventional long-range order, but an infinitesimal disorder picks out uncompensated cluster states from the multi degenerate SL regime, potentializing the intercluster disordered coupling and bringing the cluster spin-glass state. To summarize, our results suggest that the SL state combined with low levels of disorder can activate small clusters, providing hypersensitivity to the freezing process in geometrically frustrated materials and playing a key role in the glassy stabilization. We propose that this physical mechanism could be present in several geometrically frustrated materials. In particular, we discuss our results in connection to the recent experimental investigations of the Ising kagome compound Co$_3$Mg(OH)$_6$Cl$_2$.

The interplay between quantum fluctuations and disorder is investigated in a spin-glass model, in the presence of a uniform transverse field $\Gamma$, and a longitudinal random field following a Gaussian distribution with width $\Delta$. The model is studied through the replica formalism. This study is motivated by experimental investigations on the LiHo$_x$Y$_{1-x}$F$_4$ compound, where the application of a transverse magnetic field yields rather intriguing effects, particularly related to the behavior of the nonlinear magnetic susceptibility $\chi_3$, which have led to a considerable experimental and theoretical debate. We analyzed two situations, namely, $\Delta$ and $\Gamma$ considered as independent, as well as these two quantities related as proposed recently by some authors. In both cases, a spin-glass phase transition is found at a temperature $T_f$; moreover, $T_f$ decreases by increasing $\Gamma$ towards a quantum critical point at zero temperature. The situation where $\Delta$ and $\Gamma$ are related appears to reproduce better the experimental observations on the LiHo$_x$Y$_{1-x}$F$_4$ compound, with the theoretical results coinciding qualitatively with measurements of the nonlinear susceptibility. In this later case, by increasing $\Gamma$, $\chi_3$ becomes progressively rounded, presenting a maximum at a temperature $T^*$ ($T^*>T_f$). Moreover, we also show that the random field is the main responsible for the smearing of the nonlinear susceptibility, acting significantly inside the paramagnetic phase, leading to two regimes delimited by the temperature $T^*$, one for $T_fT^*$. It is argued that the conventional paramagnetic state corresponds to $T>T^*$, whereas the temperature region $T_f

We present V and R photometry of the gravitationally lensed quasars WFI2033-4723 and HE0047-1756. The data were taken by the MiNDSTEp collaboration with the 1.54 m Danish telescope at the ESO La Silla observatory from 2008 to 2012. Differential photometry has been carried out using the image subtraction method as implemented in the HOTPAnTS package, additionally using GALFIT for quasar photometry. The quasar WFI2033-4723 showed brightness variations of order 0.5 mag in V and R during the campaign. The two lensed components of quasar HE0047-1756 varied by 0.2-0.3 mag within five years. We provide, for the first time, an estimate of the time delay of component B with respect to A of $\Delta t= 7.6\pm1.8$ days for this object. We also find evidence for a secular evolution of the magnitude difference between components A and B in both filters, which we explain as due to a long-duration microlensing event. Finally we find that both quasars WFI2033-4723 and HE0047-1756 become bluer when brighter, which is consistent with previous studies., Comment: 16 pages, 15 figures, 10 tables. Accepted for publication in A&A

The behavior of the nonlinear susceptibility $\chi_3$ and its relation to the spin-glass transition temperature $T_f$, in the presence of random fields, are investigated. To accomplish this task, the Sherrington-Kirkpatrick model is studied through the replica formalism, within a one-step replica-symmetry-breaking procedure. In addition, the dependence of the Almeida-Thouless eigenvalue $\lambda_{\rm AT}$ (replicon) on the random fields is analyzed. Particularly, in absence of random fields, the temperature $T_f$ can be traced by a divergence in the spin-glass susceptibility $\chi_{\rm SG}$, which presents a term inversely proportional to the replicon $\lambda_{\rm AT}$. As a result of a relation between $\chi_{\rm SG}$ and $\chi_3$, the latter also presents a divergence at $T_f$, which comes as a direct consequence of $\lambda_{\rm AT}=0$ at $T_f$. However, our results show that, in the presence of random fields, $\chi_3$ presents a rounded maximum at a temperature $T^{*}$, which does not coincide with the spin-glass transition temperature $T_f$ (i.e., $T^* > T_f$ for a given applied random field). Thus, the maximum value of $\chi_3$ at $T^*$ reflects the effects of the random fields in the paramagnetic phase, instead of the non-trivial ergodicity breaking associated with the spin-glass phase transition. It is also shown that $\chi_3$ still maintains a dependence on the replicon $\lambda_{\rm AT}$, although in a more complicated way, as compared with the case without random fields. These results are discussed in view of recent observations in the LiHo$_x$Y$_{1-x}$F$_4$ compound., Comment: accepted for publication in PRB

Mean-field theory (MFT) is one of the main available tools for analytical calculations entailed in investigations regarding many-body systems. Recently, there have been an urge of interest in ameliorating this kind of method, mainly with the aim of incorporating geometric and correlation properties of these systems. The correlated cluster MFT (CCMFT) is an improvement that succeeded quite well in doing that for classical spin systems. Nevertheless, even the CCMFT presents some deficiencies when applied to quantum systems. In this article, we address this issue by proposing the quantum CCMFT (QCCMFT), which, in contrast to its former approach, uses general quantum states in its self-consistent mean-field equations. We apply the introduced QCCMFT to the transverse Ising model in honeycomb, square, and simple cubic lattices and obtain fairly good results both for the Curie temperature of thermal phase transition and for the critical field of quantum phase transition. Actually, our results match those obtained via exact solutions, series expansions or Monte Carlo simulations.

We propose a method to study the magnetic properties of a disordered Ising kagome lattice. The model considers small spin clusters with infinite-range disordered couplings and short-range ferromagnetic (FE) or antiferromagnetic interactions. The correlated cluster mean-field theory is used to obtain an effective single-cluster problem. A finite disorder intensity in FE kagome lattice introduces a cluster spin-glass (CSG) phase. Nevertheless, an infinitesimal disorder stabilizes the CSG behavior in the geometrically frustrated kagome system. Entropy, magnetic susceptibility and spin-spin correlation are used to describe the interplay between disorder and geometric frustration (GF). We find that GF plays an important role in the low-disorder CSG phase. However, the increase of disorder can rule out the effect of GF., Comment: 9 pages, 5 figures

The goal of the present work is to investigate the role of trivial disorder and nontrivial disorder in the three-state Hopfield model under a Gaussian random field. In order to control the nontrivial disorder, the Hebb interaction is used. This provides a way to control the system frustration by means of the parameter a=p/N, varying from trivial randomness to a highly frustrated regime, in the thermodynamic limit. We performed the thermodynamic analysis using the one-step replica-symmetry-breaking mean field theory to obtain the order parameters and phase diagrams for several strengths of a, the anisotropy constant, and the random field.

Although many models have been proposed, the physical mechanisms responsible for the formation of low-mass brown dwarfs are poorly understood. The multiplicity properties and minimum mass of the brown-dwarf mass function provide critical empirical diagnostics of these mechanisms. We present the discovery via gravitational microlensing of two very low-mass, very tight binary systems. These binaries have directly and precisely measured total system masses of 0.025 Msun and 0.034 Msun, and projected separations of 0.31 AU and 0.19 AU, making them the lowest-mass and tightest field brown-dwarf binaries known. The discovery of a population of such binaries indicates that brown dwarf binaries can robustly form at least down to masses of ~0.02 Msun. Future microlensing surveys will measure a mass-selected sample of brown-dwarf binary systems, which can then be directly compared to similar samples of stellar binaries., Comment: 7 pages, 5 figures, 3 tables, ApJ submitted

The present work studies the Ghatak-Sherrington (GS) model with the presence of a longitudinal magnetic random field (RF) $h_{i}$ following a bimodal distribution. The model considers a random bond interaction $J_{i,j}$ which follows a Gaussian distribution with mean $J_0/N$ and variance $J^2/N$. This allows us to introduce the bond disorder strength parameter $J/J_0$ to probe the combined effects of disorder coming from the random bond and the discrete RF over unusual phase transitions known as inverse transitions (ITs). The results within a mean field approximation indicate that these two types of disorder have complete distinct roles for the ITs. They indicate that bond disorder creates the necessary conditions for the presence of inverse freezing or even inverse melting depending on the bond disorder strength, while the RF tends to enforce mechanisms that destroy the ITs.

With the aim of characterizing the flux and color variations of the multiple components of the gravitationally lensed quasar UM673 as a function of time, we have performed multi-epoch and multi-band photometric observations with the Danish 1.54m telescope at the La Silla Observatory. The observations were carried out in the VRi spectral bands during four seasons (2008--2011). We reduced the data using the PSF (Point Spread Function) photometric technique as well as aperture photometry. Our results show for the brightest lensed component some significant decrease in flux between the first two seasons (+0.09/+0.11/+0.05 mag) and a subsequent increase during the following ones (-0.11/-0.11/-0.10 mag) in the V/R/i spectral bands, respectively. Comparing our results with previous studies, we find smaller color variations between these seasons as compared with previous ones. We also separate the contribution of the lensing galaxy from that of the fainter and close lensed component., Comment: 7 pages, 8 figures, 4 tables

Brown dwarfs are important objects because they may provide a missing link between stars and planets, two populations that have dramatically different formation history. In this paper, we present the candidate binaries with brown dwarf companions that are found by analyzing binary microlensing events discovered during 2004 - 2011 observation seasons. Based on the low mass ratio criterion of q < 0.2, we found 7 candidate events, including OGLE-2004-BLG-035, OGLE-2004-BLG-039, OGLE-2007-BLG-006, OGLE-2007-BLG-399/MOA-2007-BLG-334, MOA-2011-BLG-104/OGLE-2011-BLG-0172, MOA-2011-BLG-149, and MOA-201-BLG-278/OGLE-2011-BLG-012N. Among them, we are able to confirm that the companions of the lenses of MOA-2011-BLG-104/OGLE-2011-BLG-0172 and MOA-2011-BLG-149 are brown dwarfs by determining the mass of the lens based on the simultaneous measurement of the Einstein radius and the lens parallax. The measured mass of the brown dwarf companions are (0.02 +/- 0.01) M_Sun and (0.019 +/- 0.002) M_Sun for MOA-2011-BLG-104/OGLE-2011-BLG-0172 and MOA-2011-BLG-149, respectively, and both companions are orbiting low mass M dwarf host stars. More microlensing brown dwarfs are expected to be detected as the number of lensing events with well covered light curves increases with new generation searches., Comment: 10 pages, 9 figures, 4 tables

The present work studies the Ghatak-Sherrington (GS) model in the presence of a magnetic random field (RF). Previous results obtained from GS model without RF suggest that disorder and frustration are the key ingredients to produce spontaneous inverse freezing (IF). However, in this model, the effects of disorder and frustration always appear combined. In that sense, the introduction of RF allows us to study the IF under the effects of a disorder which is not a source of frustration. The problem is solved within the one step replica symmetry approximation. The results show that the first order transition between the spin glass and the paramagnetic phases, which is related to the IF for a certain range of crystal field $D$, is gradually suppressed when the RF is increased., Comment: accepted in the PRE, 6 pages, 8 figures

We present the analysis of the light curves of 9 high-magnification single-lens gravitational microlensing events with lenses passing over source stars, including OGLE-2004-BLG-254, MOA-2007-BLG-176, MOA-2007-BLG-233/OGLE-2007-BLG-302, MOA-2009-BLG-174, MOA-2010-BLG-436, MOA-2011-BLG-093, MOA-2011-BLG-274, OGLE-2011-BLG-0990/MOA-2011-BLG-300, and OGLE-2011-BLG-1101/MOA-2011-BLG-325. For all events, we measure the linear limb-darkening coefficients of the surface brightness profile of source stars by measuring the deviation of the light curves near the peak affected by the finite-source effect. For 7 events, we measure the Einstein radii and the lens-source relative proper motions. Among them, 5 events are found to have Einstein radii less than 0.2 mas, making the lenses candidates of very low-mass stars or brown dwarfs. For MOA-2011-BLG-274, especially, the small Einstein radius of $\theta_{\rm E}\sim 0.08$ mas combined with the short time scale of $t_{\rm E}\sim 2.7$ days suggests the possibility that the lens is a free-floating planet. For MOA-2009-BLG-174, we measure the lens parallax and thus uniquely determine the physical parameters of the lens. We also find that the measured lens mass of $\sim 0.84\ M_\odot$ is consistent with that of a star blended with the source, suggesting that the blend is likely to be the lens. Although we find planetary signals for none of events, we provide exclusion diagrams showing the confidence levels excluding the existence of a planet as a function of the separation and mass ratio., Comment: 14 pages, 12 figures, 5 tables

For harmonic-trapped atomic systems, we report system-independent non-adiabatic features in the response to interaction ramps. We provide results for several different systems in one, two, and three dimensions: bosonic and fermionic Hubbard models realized through optical lattices, a Bose-Einstein condensate, a fermionic superfluid and a fermi liquid. The deviation from adiabaticity is characterized through the heating or excitation energy produced during the ramp. We find that the dependence of the heat on the ramp time is sensitive to the ramp protocol but has aspects common to all systems considered. We explain these common features in terms of universal dynamics of the system size or cloud radius., Comment: v3: Published (expanded) version, 7+ pages, 4 figures. v2: Shorter, 4+ pages, 3 figures. Related preprint arXiv:1012.4492 describes similar dynamics for BEC only

Microlensing can provide a useful tool to probe binary distributions down to low-mass limits of binary companions. In this paper, we analyze the light curves of 8 binary lensing events detected through the channel of high-magnification events during the seasons from 2007 to 2010. The perturbations, which are confined near the peak of the light curves, can be easily distinguished from the central perturbations caused by planets. However, the degeneracy between close and wide binary solutions cannot be resolved with a $3\sigma$ confidence level for 3 events, implying that the degeneracy would be an important obstacle in studying binary distributions. The dependence of the degeneracy on the lensing parameters is consistent with a theoretic prediction that the degeneracy becomes severe as the binary separation and the mass ratio deviate from the values of resonant caustics. The measured mass ratio of the event OGLE-2008-BLG-510/MOA-2008-BLG-369 is $q\sim 0.1$, making the companion of the lens a strong brown-dwarf candidate., Comment: 10 figures, 6 tables, 26 pages

We present the discovery and mass measurement of the cold, low-mass planet MOA-2009-BLG-266Lb, made with the gravitational microlensing method. This planet has a mass of m_p = 10.4 +- 1.7 Earth masses and orbits a star of mass M_* = 0.56 +- 0.09 Solar masses at a semi-major axis of a = 3.2 (+1.9 -0.5) AU and an orbital period of P = 7.6 (+7.7 -1.5} yrs. The planet and host star mass measurements are enabled by the measurement of the microlensing parallax effect, which is seen primarily in the light curve distortion due to the orbital motion of the Earth. But, the analysis also demonstrates the capability to measure microlensing parallax with the Deep Impact (or EPOXI) spacecraft in a Heliocentric orbit. The planet mass and orbital distance are similar to predictions for the critical core mass needed to accrete a substantial gaseous envelope, and thus may indicate that this planet is a "failed" gas giant. This and future microlensing detections will test planet formation theory predictions regarding the prevalence and masses of such planets., Comment: 38 pages with 7 figures

aims: We present VRi photometric observations of the quadruply imaged quasar HE 0435-1223, carried out with the Danish 1.54m telescope at the La Silla Observatory. Our aim was to monitor and study the magnitudes and colors of each lensed component as a function of time. methods: We monitored the object during two seasons (2008 and 2009) in the VRi spectral bands, and reduced the data with two independent techniques: difference imaging and PSF (Point Spread Function) fitting.results: Between these two seasons, our results show an evident decrease in flux by ~0.2-0.4 magnitudes of the four lensed components in the three filters. We also found a significant increase (~0.05-0.015) in their V-R and R-i color indices. conclusions: These flux and color variations are very likely caused by intrinsic variations of the quasar between the observed epochs. Microlensing effects probably also affect the brightest "A" lensed component., Comment: 10 pages, 8 figures

We use archival data of NASA's Chandra X-ray telescope to compile an X-ray light curve of all four images of the quadruply lensed quasar Q2237+0305 (z=1.695) from January 2006 to January 2007. We fit simulated point spread functions to the four individual quasar images using Cash's C-statistic to account for the Poisson nature of the X-ray signal. The quasar images display strong flux variations up to a factor of ~4 within one month. We can disentangle the intrinsic quasar variability from flux variations due to gravitational microlensing by looking at the flux ratios of the individual quasar images. Doing this, we find evidence for microlensing in image A. In particular, the time-sequence of the flux ratio A/B in the X-ray regime correlates with the corresponding sequence in the optical monitoring by OGLE in the V-band. The amplitudes in the X-ray light curve are larger. For the most prominent peak, the increase of the X-ray ratio A/B is larger by a factor ~1.6 compared to the signal in the optical. In agreement with theory and other observations of multiply imaged quasars, this suggests that the X-ray emission region of this quasar is significantly smaller than the optical emission region., Comment: 9 pages, 5 figures, 3 tables, accepted for publication in MNRAS

We report the gravitational microlensing discovery of a sub-Saturn mass planet, MOA-2009-BLG-319Lb, orbiting a K or M-dwarf star in the inner Galactic disk or Galactic bulge. The high cadence observations of the MOA-II survey discovered this microlensing event and enabled its identification as a high magnification event approximately 24 hours prior to peak magnification. As a result, the planetary signal at the peak of this light curve was observed by 20 different telescopes, which is the largest number of telescopes to contribute to a planetary discovery to date. The microlensing model for this event indicates a planet-star mass ratio of q = (3.95 +/- 0.02) x 10^{-4} and a separation of d = 0.97537 +/- 0.00007 in units of the Einstein radius. A Bayesian analysis based on the measured Einstein radius crossing time, t_E, and angular Einstein radius, \theta_E, along with a standard Galactic model indicates a host star mass of M_L = 0.38^{+0.34}_{-0.18} M_{Sun} and a planet mass of M_p = 50^{+44}_{-24} M_{Earth}, which is half the mass of Saturn. This analysis also yields a planet-star three-dimensional separation of a = 2.4^{+1.2}_{-0.6} AU and a distance to the planetary system of D_L = 6.1^{+1.1}_{-1.2} kpc. This separation is ~ 2 times the distance of the snow line, a separation similar to most of the other planets discovered by microlensing., Comment: accepted to ApJ, 28 pages, 6 figures, 3 tables

We report the result of the analysis of a dramatic repeating gravitational microlensing event OGLE-2009-BLG-092/MOA-2009-BLG-137, for which the light curve is characterized by two distinct peaks with perturbations near both peaks. We find that the event is produced by the passage of the source trajectory over the central perturbation regions associated with the individual components of a wide-separation binary. The event is special in the sense that the second perturbation, occurring $\sim 100$ days after the first, was predicted by the real-time analysis conducted after the first peak, demonstrating that real-time modeling can be routinely done for binary and planetary events. With the data obtained from follow-up observations covering the second peak, we are able to uniquely determine the physical parameters of the lens system. We find that the event occurred on a bulge clump giant and it was produced by a binary lens composed of a K and M-type main-sequence stars. The estimated masses of the binary components are $M_1=0.69 \pm 0.11\ M_\odot$ and $M_2=0.36\pm 0.06\ M_\odot$, respectively, and they are separated in projection by $r_\perp=10.9\pm 1.3\ {\rm AU}$. The measured distance to the lens is $D_{\rm L}=5.6 \pm 0.7\ {\rm kpc}$. We also detect the orbital motion of the lens system., Comment: 18 pages, 5 figures, 1 table

In the present work it is studied the fermionic van Hemmen model for the spin glass (SG) with a transverse magnetic field $\Gamma$. In this model, the spin operators are written as a bilinear combination of fermionic operators, which allows the analysis of the interplay between charge and spin fluctuations in the presence of a quantum spin flipping mechanism given by $\Gamma$. The problem is expressed in the fermionic path integral formalism. As results, magnetic phase diagrams of temperature versus the ferromagnetic interaction are obtained for several values of chemical potential $\mu$ and $\Gamma$. The $\Gamma$ field suppresses the magnetic orders. The increase of $\mu$ alters the average occupation per site that affects the magnetic phases. For instance, the SG and the mixed SG+ferromagnetic phases are also suppressed by $\mu$. In addition, $\mu$ can change the nature of the phase boundaries introducing a first order transition., Comment: 9 pages, 4 figures, accepted for publication in Phys. Lett. A

We present high-precision photometry of three transits of the extrasolar planetary system WASP-2, obtained by defocussing the telescope, and achieving point-to-point scatters of between 0.42 and 0.73 mmag. These data are modelled using the JKTEBOP code, and taking into account the light from the recently-discovered faint star close to the system. The physical properties of the WASP-2 system are derived using tabulated predictions from five different sets of stellar evolutionary models, allowing both statistical and systematic errorbars to be specified. We find the mass and radius of the planet to be M_b = 0.847 +/- 0.038 +/- 0.024 Mjup and R_b = 1.044 +/- 0.029 +/- 0.015 Rjup. It has a low equilibrium temperature of 1280 +/- 21 K, in agreement with a recent finding that it does not have an atmospheric temperature inversion. The first of our transit datasets has a scatter of only 0.42 mmag with respect to the best-fitting light curve model, which to our knowledge is a record for ground-based observations of a transiting extrasolar planet., Comment: Accepted for publication in MNRAS. 9 pages, 3 figures, 10 tables

We propose a scheme to entangle two mechanical nanocantilevers through indirect interactions mediated by a gas of ultra cold atoms. We envisage a system of nanocantilevers magnetically coupled to a Bose-Einstein condensate of atoms and focus on studying the dark states of the system. These dark states are entangled states of the two nanocantilevers, with no coupling to the atomic condensate. In the absence of dissipation, the degree of entanglement is found to oscillate with time, while if dissipation is included, the system is found to relax to a statistical mixture of dark states which remains time independent until the inevitable thermal dephasing destroys the nanocantilever coherence. This opens up the possibility of achieving long-lived entangled nanocantilever states., Comment: 10 pages, 8 figures

We present here a theoretical model in order to describe the competition between the Kondo effect and the spin glass behavior. The spin glass part of the starting Hamiltonian contains Ising spins with an intersite exchange interaction given by the local van Hemmen model, while the Kondo effect is described as usual by the intrasite exchange $J_K$. We obtain, for large $J_K$ values, a Kondo phase and, for smaller $J_K$ values, a succession, with decreasing, Comment: 14 pages, 4 figures, accepted for publication in Phys. Rev. B

In this work it is studied the Hopfield fermionic spin glass model which allows interpolating from trivial randomness to a highly frustrated regime. Therefore, it is possible to investigate whether or not frustration is an essential ingredient which would allow this magnetic disordered model to present naturally inverse freezing by comparing the two limits, trivial randomness and highly frustrated regime and how different levels of frustration could affect such unconventional phase transition. The problem is expressed in the path integral formalism where the spin operators are represented by bilinear combinations of Grassmann variables. The Grand Canonical Potential is obtained within the static approximation and one-step replica symmetry breaking scheme. As a result, phase diagrams temperature {\it versus} the chemical potential are obtained for several levels of frustration. Particularly, when the level of frustration is diminished, the reentrance related to the inverse freezing is gradually suppressed., Comment: 10 pages, 4 figures, accepted for publication in Phys. Rev. B

We present high-precision photometry of five consecutive transits of WASP-18, an extrasolar planetary system with one of the shortest orbital periods known. Through the use of telescope defocussing we achieve a photometric precision of 0.47 to 0.83 mmag per observation over complete transit events. The data are analysed using the JKTEBOP code and three different sets of stellar evolutionary models. We find the mass and radius of the planet to be M_b = 10.43 +/- 0.30 +/- 0.24 Mjup R_b = 1.165 +/- 0.055 +/- 0.014 Rjup (statistical and systematic errors) respectively. The systematic errors in the orbital separation and the stellar and planetary masses, arising from the use of theoretical predictions, are of a similar size to the statistical errors and set a limit on our understanding of the WASP-18 system. We point out that seven of the nine known massive transiting planets (M_b > 3 Mjup) have eccentric orbits, whereas significant orbital eccentricity has been detected for only four of the 46 less massive planets. This may indicate that there are two different populations of transiting planets, but could also be explained by observational biases. Further radial velocity observations of low-mass planets will make it possible to choose between these two scenarios., Comment: 6 pages, 2 figures, 4 tables. Accepted for publication in ApJ. Data can be obtained from http://www.astro.keele.ac.uk/~jkt/

In the presence of a laser-induced spin-orbit coupling an interacting ultra cold spinor Bose-Einstein condensate may acquire a quasi-relativistic character described by a non-linear Dirac-like equation. We show that as a result of the spin-orbit coupling and the non-linearity the condensate may become self-trapped, resembling the so-called chiral confinement, previously studied in the context of the massive Thirring model. We first consider 1D geometries where the self-confined condensates present an intriguing sinusoidal dependence on the inter-particle interactions. We further show that multi-dimensional chiral-confinement is also possible under appropriate feasible laser arrangements, and discuss the properties of 2D and 3D condensates, which differ significantly from the 1D case., Comment: 4 pages

The physics of disordered alloys, such as typically the well known case of CeNi1-xCux alloys, showing an interplay among the Kondo effect, the spin glass state and a magnetic order, has been studied firstly within an average description like in the Sherrington-Kirkpatrick model. Recently, a theoretical model (PRB 74, 014427 (2006)) involving a more local description of the intersite interaction has been proposed to describe the phase diagram of CeNi1-xCux. This alloy is an example of the complex interplay between Kondo effect and frustration in which there is in particular the onset of a cluster-glass state. Although the model given in Ref. PRB 74, 014427 (2006) has reproduced the different phases relatively well, it is not able to describe the cluster-glass state. We study here the competition between the Kondo effect and a cluster glass phase within a Kondo Lattice model with an inter-cluster random Gaussian interaction. The inter-cluster term is treated within the cluster mean-field theory for spin glasses, while, inside the cluster, an exact diagonalisation is performed including inter-site ferromagnetic and intra-site Kondo interactions. The cluster glass order parameters and the Kondo correlation function are obtained for different values of the cluster size, the intra-cluster ferromagnetic coupling and the Kondo intra-site coupling. We obtain, for instance, that the increase of the Kondo coupling tends to destroy the cluster glass phase., Comment: 6 pages, 2 figures, Accepted for publication in Physica B

The stability of spin-glass (SG) phase is analyzed in detail for a fermionic Ising SG (FISG) model in the presence of a magnetic transverse field $\Gamma$. The fermionic path integral formalism, replica method and static approach have been used to obtain the thermodynamic potential within one step replica symmetry breaking ansatz. The replica symmetry (RS) results show that the SG phase is always unstable against the replicon. Moreover, the two other eigenvalues $\lambda_{\pm}$ of the Hessian matrix (related to the diagonal elements of the replica matrix) can indicate an additional instability to the SG phase, which enhances when $\Gamma$ is increased. Therefore, this result suggests that the study of the replicon can not be enough to guarantee the RS stability in the present quantum FISG model, especially near the quantum critical point. In particular, the FISG model allows changing the occupation number of sites, so one can get a first order transition when the chemical potential exceeds a certain value. In this region, the replicon and the $\lambda_{\pm}$ indicate instability problems for the SG solution close to all range of first order boundary., Comment: 15 pages, 4 figures, accepted in Physica A

Ultra-cold atoms which are subject to ultra-relativistic dynamics are investigated. By using optically induced gauge potentials we show that the dynamics of the atoms is governed by a Dirac type equation. To illustrate this we study the trembling motion of the centre of mass for an effective two level system, historically called Zitterbewegung. Its origin is described in detail, where in particular the role of the finite width of the atomic wave packets is seen to induce a damping of both the centre of mass dynamics and the dynamics of the populations of the two levels., Comment: 6 pages, 4 figures

We investigate the inverse freezing in the fermionic Ising spin-glass (FISG) model in a transverse field $\Gamma$. The grand canonical potential is calculated in the static approximation, replica symmetry and one-step replica symmetry breaking Parisi scheme. It is argued that the average occupation per site $n$ is strongly affected by $\Gamma$. As consequence, the boundary phase is modified and, therefore, the reentrance associated with the inverse freezing is modified too., Comment: 6 pages, 3 figures, accepted for publication in PRB

We present a general scheme to determine the loss-free adiabatic eigensolutions (dark-state polaritons) of the interaction of multiple probe laser beams with a coherently driven atomic ensemble under conditions of electromagnetically induced transparency. To this end we generalize the Morris-Shore transformation to linearized Heisenberg-Langevin equations describing the coupled light-matter system in the weak excitation limit. For the simple lambda-type coupling scheme the generalized Morris-Shore transformation reproduces the dark-state polariton solutions of slow light. Here we treat a closed-loop dual-V scheme wherein two counter-propagating control fields generate a quasi stationary pattern of two counter-propagating probe fields -- so-called stationary light. We show that contrary to previous predictions,there exists a single unique dark-state polariton; it obeys a simple propagation equation., Comment: 6 pages, 2 figures

The Doniach's diagram has been originally proposed to describe the competition between the local Kondo effect and the intersite RKKY interactions in cerium compounds. Here we discuss the extension of this diagram to different variations of Kondo lattice model. We consider a) ordered cerium compounds where the competition between magnetic order and Kondo effect plays an important role, as $CeRh_2Si_2$, b) disordered cerium systems with competing spin glass phase, magnetic ordered phases and a Kondo phase, as the heavy fermion cerium alloy $CeCu_xNi_{1-x}$ and, c) uranium compounds where a coexistence between Kondo effect and ferromagnetic order has been observed, as UTe. We show that all these cases can be described by a generalized Doniach phase diagram., Comment: Presented in the Latin American Workshop on Magnetism and Magnetic Materials (LAW3M) Rio de Janeiro, Brazil, August 12-16, 2007. Proceedings to be published in JMMM

The one-step replica symmetry breaking (RSB) is used to study a two-sublattice fermionic infinite-range Ising spin glass (SG) model in a transverse field $\Gamma$. The problem is formulated in a Grassmann path integral formalism within the static approximation. In this model, a parallel magnetic field $H$ breaks the symmetry of the sublattices. It destroys the antiferromagnetic (AF) order, but it can favor the nonergodic mixed phase (SG+AF) characterizing an asymmetric RSB region. In this region, intra-sublattice disordered interactions $V$ increase the difference between the RSB solutions of each sublattice. The freezing temperature shows a higher increase with $H$ when $V$ enhances. A discontinue phase transition from the replica symmetry (RS) solution to the RSB solution can appear with the presence of an intra-sublattice ferromagnetic average coupling. The $\Gamma$ field introduces a quantum spin flip mechanism that suppresses the magnetic orders leading them to quantum critical points. Results suggest that the quantum effects are not able to restore the RS solution. However, in the asymmetric RSB region, $\Gamma$ can produce a stable RS solution at any finite temperature for a particular sublattice while the other sublattice still presents RSB solution for the special case in which only the intra-sublattice spins couple with disordered interactions., Comment: 11 pages, 8 figures, accepted for publication in Phys. Rev. B

The light--matter-wave Sagnac interferometer based on ultra-slow light proposed recently in (Phys. Rev. Lett. 92, 253201 (2004)) is analyzed in detail. In particular the effect of confining potentials is examined and it is shown that the ultra-slow light attains a rotational phase shift equivalent to that of a matter wave, if and only if the coherence transfer from light to atoms associated with slow light is associated with a momentum transfer and if an ultra-cold gas in a ring trap is used. The quantum sensitivity limit of the Sagnac interferometer is determined and the minimum detectable rotation rate calculated. It is shown that the slow-light interferometer allows for a significantly higher signal-to-noise ratio as possible in current matter-wave gyroscopes., Comment: 12 pages, 6 figures

The competition between spin glass, ferromagnetism and Kondo effect is analysed here in a Kondo lattice model with an inter-site random coupling $J_{ij}$ between the localized magnetic moments given by a generalization of the Mattis model which represents an interpolation between ferromagnetism and a highly disordered spin glass. Functional integral techniques with Grassmann fields have been used to obtain the partition function. The static approximation and the replica symmetric ansatz have also been used. The solution of the problem is presented as a phase diagram giving $T/{J}$ {\it versus} $J_K/J$ where $T$ is the temperature, $J_{K}$ and ${J}$ are the strengths of the intrasite Kondo and the intersite random couplings, respectively. If $J_K/{J}$ is small, when temperature is decreased, there is a second order transition from a paramagnetic to a spin glass phase. For lower $T/{J}$, a first order transition appears between the spin glass phase and a region where there are Mattis states which are thermodynamically equivalent to the ferromagnetism. For very low ${T/{J}}$, the Mattis states become stable. On the other hand, it is found as solution a Kondo state for large $J_{K}/{J}$ values. These results can improve the theoretical description of the well known experimental phase diagram of $CeNi_{1-x}Cu_{x}$., Comment: 17 pages, 5 figures, accepted Phys. Rev. B

The competition among spin glass (SG), antiferromagnetism (AF) and local pairing superconductivity (PAIR) is studied in a two-sublattice fermionic Ising spin glass model with a local BCS pairing interaction in the presence of an applied magnetic transverse field $\Gamma$. In the present approach, spins in different sublattices interact with a Gaussian random coupling with an antiferromagnetic mean $J_0$ and standard deviation $J$. The problem is formulated in the path integral formalism in which spin operators are represented by bilinear combinations of Grassmann variables. The saddle-point Grand Canonical potential is obtained within the static approximation and the replica symmetric ansatz. The results are analysed in phase diagrams in which the AF and the SG phases can occur for small $g$ ($g$ is the strength of the local superconductor coupling written in units of $J$), while the PAIR phase appears as unique solution for large $g$. However, there is a complex line transition separating the PAIR phase from the others. It is second order at high temperature that ends in a tricritical point. The quantum fluctuations affect deeply the transition lines and the tricritical point due to the presence of $\Gamma$., Comment: 16 pages, 6 figures, accepted Eur. Phys. J. B