Search

While there are many well-known and extensively tested results involving diffusion-limited binary reactions, reactions involving subdiffusive reactant species are far less understood. Subdiffusive motion is characterized by a mean square displacement $ \sim t^\gamma$ with $0<\gamma<1$. Recently we calculated the asymptotic survival probability $P(t)$ of a (sub)diffusive particle ($\gamma^\prime$) surrounded by (sub)diffusive traps ($\gamma$) in one dimension. These are among the few known results for reactions involving species characterized by different anomalous exponents. Our results were obtained by bounding, above and below, the exact survival probability by two other probabilities that are asymptotically identical (except when $\gamma^\prime=1$ and $0<\gamma<2/3$). Using this approach, we were not able to estimate the time of validity of the asymptotic result, nor the way in which the survival probability approaches this regime. Toward this goal, here we present a detailed comparison of the asymptotic results with numerical simulations. In some parameter ranges the asymptotic theory describes the simulation results very well even for relatively short times. However, in other regimes more time is required for the simulation results to approach asymptotic behavior, and we arrive at situations where we are not able to reach asymptotia within our computational means. This is regrettably the case for $\gamma^\prime=1$ and $0<\gamma<2/3$, where we are therefore not able to prove or disprove even conjectures about the asymptotic survival probability of the particle., Comment: 15 pages, 10 figures, submitted to Journal of Physics: Condensed Matter; special issue on Chemical Kinetics Beyond the Textbook: Fluctuations, Many-Particle Effects and Anomalous Dynamics, eds. K.Lindenberg, G.Oshanin and M.Tachiya

We calculate the survival probability of a stationary target in one dimension surrounded by diffusive or subdiffusive traps of time-dependent density. The survival probability of a target in the presence of traps of constant density is known to go to zero as a stretched exponential whose specific power is determined by the exponent that characterizes the motion of the traps. A density of traps that grows in time always leads to an asymptotically vanishing survival probability. Trap evanescence leads to a survival probability of the target that may be go to zero or to a finite value indicating a probability of eternal survival, depending on the way in which the traps disappear with time.

We have studied the spin anisotropy in spin-singlet ground state compounds and the magnetic chirality, as measured by inelastic polarized neutron scattering techniques, in the chain-sublattice of Sr14Cu24O41. In-plane and out of plane magnetic fluctuations are measured to be anisotropic and further discussed in the light of the current hypothesis of spin-orbit coupling. We show that under appropriate conditions of magnetic field and neutron polarization, the \textit{trivial} magnetic chirality selects only one of the Zeeman splitted triplet states for scattering and erases the other one that posses opposite helicity. Our analysis pertains to previous studies on dynamical magnetic chirality and chiral critical exponents, where the ground state is chiral itself, the so-called \textit{non-trivial} dynamical magnetic chirality. As it turns out, both \textit{trivial} and \textit{non-trivial} dynamical magnetic chirality have identical selection rules for inelastic polarized neutron scattering experiments and it is not at all evident that they can be distinguished in a paramagnetic compound., Comment: 15 pages, 10 figures, submitted to Phys. Rev. B

Here we show that the low temperature phase of magnetite is associated with an effective, although fractional, ordering of the charge. Evidence and a quantitative evaluation of the atomic charges are achieved by using resonant x-ray diffraction (RXD) experiments whose results are further analyzed with the help of ab initio calculations of the scattering factors involved. By confirming the results obtained from X-ray crystallography we have shown that RXD is able to probe quantitatively the electronic structure in very complex oxides, whose importance covers a wide domain of applications., Comment: 4 pages 4 figures, accepted for publication in PRL

Numerical Simulations of the random phase sine-Gordon model suffer from strong finite size effects preventing the non-Gaussian $\log^2 r$ component of the spatial correlator from following the universal infinite volume prediction. We show that a finite size prediction based on perturbative Renormalisation Group (RG) arguments agrees well with new high precision simulations for small coupling and close to the critical temperature., Comment: 13 pages, 3 ps figures. Extensive new numerical simulations

In conventional spin glasses, magnetic interaction is not strongly anisotropic and the entire spin system is believed to be frozen below the spin-glass transition temperature. In La2Cu0.94Li0.06O4, for which the in-plane exchange interaction dominates the interplane one, only a fraction of spins with antiferromagnetic correlations extending to neighboring planes become spin-glass. The remaining spins with only in-plane antiferromagnetic correlations remain spin-liquid at low temperature. Such a novel partial spin freezing out of a two-dimensional spin-liquid observed in this cold neutron scattering study is likely due to a delicate balance between disorder and quantum fluctuations in the quasi-two dimensional S=1/2 Heisenberg system., Comment: 6 pages, 4 figures

Dedicated machines designed for specific computational algorithms can outperform conventional computers by several orders of magnitude. In this note we describe {\it Ianus}, a new generation FPGA based machine and its basic features: hardware integration and wide reprogrammability. Our goal is to build a machine that can fully exploit the performance potential of new generation FPGA devices. We also plan a software platform which simplifies its programming, in order to extend its intended range of application to a wide class of interesting and computationally demanding problems. The decision to develop a dedicated processor is a complex one, involving careful assessment of its performance lead, during its expected lifetime, over traditional computers, taking into account their performance increase, as predicted by Moore's law. We discuss this point in detail.

A simple position probability density formulation is presented for the motion of a particle in a spherically symmetric potential. The approach provides an alternative to Newtonian methods for presentation in an elementary course, and requires only elementary algebra and one tabulated integral. The method is applied to compute the distributions for the Kepler-Coulomb and isotropic harmonic oscillator potentials. Formulas are also deduced for the average values for powers of the radial coordinate, and applied to describe perturbations to these systems. The classical results are also compared with quantum mechanical calculations using the Einstein-Brillouin-Keller semiclassical quantization., Comment: 14 pages, 2 figures

The Landau-Ginzburg-Wilson paradigm for critical phenomena is spectacularly successful whenever the critical temperature is finite and all fluctuation modes, with characteristic energies much smaller than the thermal energy, obey classical statistics. In zero-temperature quantum critical phenomena, classical thermal fluctuations are replaced by zero-point quantum fluctuations and quantum-mechanical generalization of the Landau-Ginzburg-Wilson paradigm has been a central topic in condensed-matter physics. In this neutron-scattering study on spin fluctuations near the quantum critical point induced by hole-doping in La2CuO4 (Li doping concentration from 0.04 to 0.1), the phase boundary for quantum crossover expected from the generalized quantum theory for critical phenomena was observed for the first time. Furthermore, critical exponent and scaling function become anomalous near the quantum critical point, which has not been expected in current theories., Comment: 4 pages; 4 color figs; 1 table

The phase diagram of the simplest approximation to Double-Exchange systems, the bosonic Double-Exchange model with antiferromagnetic super-exchange coupling, is fully worked out by means of Monte Carlo simulations, large-N expansions and Variational Mean-Field calculations. We find a rich phase diagram, with no first-order phase transitions. The most surprising finding is the existence of a segment like ordered phase at low temperature for intermediate AFM coupling which cannot be detected in neutron-scattering experiments. This is signaled by a maximum (a cusp) in the specific heat. Below the phase-transition, only short-range ordering would be found in neutron-scattering. Researchers looking for a Quantum Critical Point in manganites should be wary of this possibility. Finite-Size Scaling estimates of critical exponents are presented, although large scaling corrections are present in the reachable lattice sizes., Comment: 17 pages, 14 figures

We review some recent results on finite dimensional spin glasses by studying recent numerical simulations and their relationship with experiments. In particular we will show results obtained at zero and non zero temperature, focusing in the low temperature properties of the model, and contrast them with different pictures of the low temperature phase of spin glasses: Replica Symmetry Breaking, Droplet Model and Trivial-Not-Trivial Scenario., Comment: Review article to appear in ``Advances in Condensed Matter and Statistical Mechanics", Ed. E. Korutcheva and R. Cuerno. To be published by Nova Science Publishers. 40 pages. 18 eps/ps figures. Updated references

We show that in mixed-valence 3d transition metal oxides undergoing a structural transition, the low temperature phase results from an effective ordering of the charge. This arrangement and the quantitative evaluation of the atomic charges are determined by using resonant x-ray scattering experiments further analyzed with the help of ab initio calculations of the corresponding scattering factors. We have found that this reorganization concerns only a small fraction of electron and is necessary to reconcile all the experimental data., Comment: 4 pages, 2 figures

It is shown that a bosonic formulation of the double-exchange model, one of the classical models for magnetism, generates dynamically a gauge-invariant phase in a finite region of the phase diagram. We use analytical methods, Monte Carlo simulations and Finite-Size Scaling analysis. We study the transition line between that region and the paramagnetic phase. The numerical results show that this transition line belongs to the Universality Class of the Antiferromagnetic RP(2) model. The fact that one can define a Universality Class for the Antiferromagnetic RP(2) model, different from the one of the O(N) models, is puzzling and somehow contradicts naive expectations about Universality., Comment: 13 pages, 3 figures

We study the fluctuation-dissipation relations for a three dimensional Ising spin glass in a magnetic field both in the high temperature phase as well as in the low temperature one. In the region of times simulated we have found that our results support a picture of the low temperature phase with broken replica symmetry, but a droplet behavior can not be completely excluded., Comment: 9 pages, 11 ps figures, revtex. Final version to be published in Phys. Rev. B

We compare ground state properties of 3D Ising Spin Glasses with Gaussian couplings with results from off-equilibrium numerical simulations at non zero (but low) temperatures. We find that the non-zero temperature properties of the system smoothly connect to the T=0 behavior, confirming the point of view that results established at T=0 typically also give relevant information about the $T\ne 0$ physics of the system., Comment: 14 pages and 4 ps figures

Anomalous x-ray diffraction studies show that the charge ordering in $\alpha^\prime$-NaV$_2$O$_5$ is of zig-zag type in all vanadium ladders. We have found that there are two models of the stacking of layers along \emph{c-}direction, each of them consisting of 2 degenerated patterns, and that the experimental data is well reproduced if the 2 patterns appears simultaneously. We believe that the low temperature structure contains stacking faults separating regions corresponding to the four possible patterns., Comment: Submitted to Phys. Rev. Lett., 4 pages, 4 eps figures inserted in the text

Using high-resolution X-ray scattering techniques, we measure the variation, q(x), of the position in reciprocal space of the CDW satellite, in the sliding state, along the length of NbSe_3 whiskers. We show that structural defects and intentionally X-ray radiation-damaged regions increase locally the CDW pinning force, and induce CDW phase distortions which are consistent with those observed near contacts. Using the semi-microscopic model from Brazovskii describing the normal-condensed carrier conversion, with spatially varying parameters, we account for the experimental spatial dependence of the CDW phase gradient near both types of defects.

We report high-resolution neutron inelastic scattering experiments on the spin excitations of NaV2O5. Below Tc, two branches associated with distinct energy gaps are identified. From the dispersion and intensity of the spin excitation modes, we deduce the precise zig-zag charge distribution on the ladder rungs and the corresponding charge order (about 0.6). We argue that the spin gaps observed in the low-T phase of this compound are primarily due to the charge transfer., Comment: 4 pages, 5 figures, to appear in Phys. Rev. Lett

We have simulated, using parallel tempering, the three dimensional Ising spin glass model with binary couplings in a helicoidal geometry. The largest lattice (L=20) has been studied using a dedicated computer (the SUE machine). We have obtained, measuring the correlation length in the critical region, a strong evidence for a second-order finite temperature phase transition ruling out other possible scenarios like a Kosterlitz-Thouless phase transition. Precise values for the $\nu$ and $\eta$ critical exponents are also presented., Comment: RevTex; 12 pages plus 5 ps figures. Final version to be published in PRB

We claim that the analysis presented by Gaulin et al. (Phys. Rev. Lett. 84, 3446 (2000)) does not prove the two-dimensional character of the transition in NaV2O5 nor the charge ordering mechanism of the transition., Comment: 1 page

We present a high statistic systematic study of the overlap correlation function well below the critical temperature in the three dimensional Gaussian spin glass. The off-equilibrium correlation function has been studied confirming the power law behavior for the dynamical correlation length. In particular we have computed the dynamical critical exponent $z$ in a wide range of temperatures, $0.35 \le T \le 0.9$, obtaining a dependence $z(T)=6.2/T$ in a very good agreement with recent experiments. Moreover, we report a study of the violation of the fluctuation-dissipation theorem for very low temperatures $T=0.5$ and $T=0.35$. All our numerical results avoid a droplet model interpretation even when $T$ is as low as $T=0.35$., Comment: LaTeX, 14 pages and 5 figures. A minor arithmetic error corrected and references updated

We show analytically that the perturbative expansion for the free energy of the zero dimensional (quenched) disordered Ising model is Borel-summable in a certain range of parameters, provided that the summation is carried out in two steps: first, in the strength of the original coupling of the Ising model and subsequently in the variance of the quenched disorder. This result is illustrated by some high-precision calculations of the free energy obtained by a straightforward numerical implementation of our sequential summation method., Comment: LaTeX, 12 pages and 4 figures

We have studied numerically the effect of quenched site dilution on a first order phase transition in three dimensions. We have simulated the site diluted three states Potts model studying in detail the second order region of its phase diagram. We have found that the $\nu$ exponent is compatible with the one of the three dimensional diluted Ising model whereas the $\eta$ exponent is definitely different., Comment: RevTex. 6 pages and 6 postscript figures

We discuss replica symmetry breaking (RSB) in spin glasses. We update work in this area, from both the analytical and numerical points of view. We give particular attention to the difficulties stressed by Newman and Stein concerning the problem of constructing pure states in spin glass systems. We mainly discuss what happens in finite-dimensional, realistic spin glasses. Together with a detailed review of some of the most important features, facts, data, and phenomena, we present some new theoretical ideas and numerical results. We discuss among others the basic idea of the RSB theory, correlation functions, interfaces, overlaps, pure states, random field, and the dynamical approach. We present new numerical results for the behaviors of coupled replicas and about the numerical verification of sum rules, and we review some of the available numerical results that we consider of larger importance (for example, the determination of the phase transition point, the correlation functions, the window overlaps, and the dynamical behavior of the system)., Comment: 48 pages, 21 figures. v2: the published version

We study the off-equilibrium critical dynamics of the three dimensional diluted Ising model. We compute the dynamical critical exponent $z$ and we show that it is independent of the dilution only when we take into account the scaling-corrections to the dynamics. Finally we will compare our results with the experimental data., Comment: Final Version, 5 Latex pages (RevTeX) plus 3 eps figures

We consider a microcanonical local algorithm to be applied on the $\pm J$ spin glass model. We have compared the results coming from a microcanonical Monte Carlo simulation with those from a canonical one: Thermalization times, spin glass susceptibilities and Binder parameters. For a fixed lattice size we found different results between the two thermodynamic ensembles, which tend to vanish at bigger volumes. Moreover, microcanonical thermalization times are longer than the canonical ones. Finally we have checked that one of the Guerra relations is satisfied with good precision for the two largest lattices., Comment: Revised version. Latex 14 pages, 6 figures. To be published in Comput. Phys. Commun

In a recent letter Moore et al. claim to exhibit evidence for a non-mean-field behavior of the $3d$ Ising spin glass. We show that their claim is insubstantial, and by analyzing in detail the behavior of the Migdal-Kadanoff approximation (MKA) as compared to the behavior of the Edwards-Anderson (EA) spin glass we find further evidence of a mean-field like behavior of the $3d$ spin glass., Comment: 1 page comment including one postscript figure

Below about 150 K, the spin arrangement in the chain arrays of Sr14Cu24O41 is shown to develop in two dimensions (2D). Both the correlations and the dispersion of the observed elementary excitations agree well with a model of interacting dimers. Along the chains, the intra- and inter-dimer distances are equal to 2 and about 3 times the distance (c) between neighboring Cu ions. While the intra-dimer coupling is J about 10 meV, the inter-dimer couplings along and between the chains are of comparable strenght, J// about -1.1 meV and Jperp about 1.7 meV, respectively. This remarkable 2D arrangement satisfies the formal Cu valence of the undoped compound. Our data suggest also that it is associated with a relative sliding of one chain with respect to the next one, which, as T decreases, develops in the chain direction. A qualitative analysis shows that nearest inter-dimer spin correlations are ferromagnetic, which, in such a 2D structure, could well result from frustration effects., Comment: 4 pages, 5 figures, submitted to Phys.Rev.B, date of receipt 29 June 1998

Using Finite-Size Scaling techniques we obtain accurate results for critical quantities of the Ising model and the site percolation, in three dimensions. We pay special attention in parameterizing the corrections-to-scaling, what is necessary to put the systematic errors below the statistical ones., Comment: 12 pages plus 2 figures. Minor corrections added

We study analytically the logarithmic corrections to the critical exponents of the critical behavior of correlation length, susceptibility and specific heat for the temperature and the finite-size scaling behavior, for a generic $\phi^3$ theory at its upper critical dimension (six). We have also computed the leading correction to scaling as a function of the lattice size. We distinguish the obtained formulas to the following special cases: percolation, Lee-Yang (LY) singularities and $m$-component spin glasses. We have compared our results for the Ising spin glass case with numerical simulations finding a very good agreement. Finally, and using the results obtained for the Lee-Yang singularities in six dimensions, we have computed the logarithmic corrections to the singular part of the free energy for lattice animals in eight dimensions., Comment: 18 pages. We have extended the computation to lattice animals in eight dimensions. To be published in Journal of Physics A

We compute numerically small window overlaps in the three dimensional Edwards Anderson spin glass. We show that they behave in the way implied by the Replica Symmetry Breaking Ansatz, that they do not qualitatively differ from the full volume overlap and do not tend to a trivial function when increasing the lattice volume. On the contrary we show they are affected by small finite volume effects, and are interesting tools for the study of the features of the spin glass phase., Comment: 9 pages plus 5 figures

We study the phase diagram of the site-diluted Ising model in a wide dilution range, through Monte Carlo simulations and Finite-Size Scaling techniques. Our results for the critical exponents and universal cumulants turn out to be dilution-independent, but only after a proper infinite volume extrapolation, taking into account the leading corrections-to-scaling terms., Comment: 17 pages, 5 postscript figures

We characterize numerically the properties of the phase transition of the three dimensional Ising spin glass with Gaussian couplings and of the low temperature phase. We compute critical exponents on large lattices. We study in detail the overlap probability distribution and the equilibrium overlap-overlap correlation functions. We find a clear agreement with off-equilibrium results from previous work. These results strongly support the existence of a continuous spontaneous replica symmetry breaking in three dimensional spin glasses., Comment: 30 pages and 17 figures. Final version to be published in PRB