Search

We study the fixed points of outer-totalistic cellular automata on sparse random regular graphs. These can be seen as constraint satisfaction problems, where each variable must adhere to the same local constraint, which depends solely on its state and the total number of its neighbors in each possible state. Examples of this setting include classical problems such as independent sets or assortative/dissasortative partitions. We analyze the existence and number of fixed points in the large system limit using the cavity method, under both the replica symmetric (RS) and one-step replica symmetry breaking (1RSB) assumption. This method allows us to characterize the structure of the space of solutions, in particular, if the solutions are clustered and whether the clusters contain frozen variables. This last property is conjectured to be linked to the typical algorithmic hardness of the problem. We bring experimental evidence for this claim by studying the performance of the belief-propagation reinforcement algorithm, a message-passing-based solver for these constraint satisfaction problems. [ABSTRACT FROM AUTHOR]

We have studied the peculiarities of electron transport in one-dimensional disordered chain at the presence of correlations between on-site interaction and tunneling integrals. In the considered models, the disorder in host-lattice sites positions is caused by presence of defects, impurities, existence of electron-phonon interaction, etc. It is shown that for certain combination of parameters the localization of electron state inherited by a various of 1D disordered systems disappears, and electron transport becomes possible. The parameters of this transport are established. [ABSTRACT FROM AUTHOR]

We consider the continuum version of the random field Ising model in one dimension: this model arises naturally as weak disorder scaling limit of the original Ising model. Like for the Ising model, a spin configuration is conveniently described as a sequence of spin domains with alternating signs (domain-wall structure). We show that for fixed centered external field and as spin-spin couplings become large, the domain-wall structure scales to a disorder dependent limit that coincides with the infinite disorder fixed point process introduced by D. S. Fisher in the context of zero temperature quantum Ising chains. In particular, our results establish a number of predictions that one can find in Fisher et al. (Phys Rev E 64:41, 2001). The infinite disorder fixed point process for centered external field is equivalently described in terms of the process of suitably selected extrema of a Brownian trajectory introduced and studied by Neveu and Pitman (in: Séminaire de probabilités XXIII. Lecture notes in mathematics, vol 1372, pp 239–247, 1989). This characterization of the infinite disorder fixed point is one of the important ingredients of our analysis. [ABSTRACT FROM AUTHOR]

Biological mixtures, such as the cellular cytoplasm, are composed of a large number of different components. From this heterogeneity, ordered mesoscopic structures emerge, such as liquid phases with controlled composition. The competition of these structures for the same components raises several questions: what types of interactions allow the retrieval of multiple ordered mesoscopic structures, and what are the physical limitations for the retrieval of said structures. In this work, we develop an analytically tractable model for multicomponent liquids capable of retrieving states with target compositions. We name this model the liquid Hopfield model in reference to corresponding work in the theory of associative neural networks. In this model, we show that nonlinear repulsive interactions are a general requirement for retrieval of target structures. We demonstrate that this is because liquid mixtures at low temperatures tend to transition to phases with few components, a phenomenon that we term localization. Taken together, our results reveal a trade-off between retrieval and localization phenomena in liquid mixtures, and pave the way for other connections between the phenomenologies of neural computation and liquid mixtures. [ABSTRACT FROM AUTHOR]

The influence of random fields on phase transitions in disordered systems has been studied using an exactly solvable model as an example. The value of the critical dimension d cr = 6 has been found, and the existence of a dimensional shift d ′ = d - 2 has been established, which transforms the value of the critical indices of systems with random fields into the value of the critical indices of pure systems of the corresponding model. The phenomenological generalization of the model has been made taking into account the additional critical index θ associated with violation of scale invariance. [ABSTRACT FROM AUTHOR]

We consider the Gaussian interface model in the presence of random external fields, that is the finite volume (random) Gibbs measure on R Λ N , Λ N = [ - N , N ] d ∩ Z d with Hamiltonian H N (ϕ) = 1 4 d ∑ x ∼ y (ϕ (x) - ϕ (y)) 2 - ∑ x ∈ Λ N η (x) ϕ (x) and 0-boundary conditions. { η (x) } x ∈ Z d is a family of i.i.d. symmetric random variables. We study how the typical maximal height of a random interface is modified by the addition of quenched bulk disorder. We show that the asymptotic behavior of the maximum changes depending on the tail behavior of the random variable η (x) when d ≥ 5 . In particular, we identify the leading order asymptotics of the maximum. [ABSTRACT FROM AUTHOR]

We apply a real-space block renormalization group approach to study the critical properties of the random transverse-field Ising spin chain with multispin interactions. First, we recover the known properties of the traditional model with two-spin interactions by applying the renormalization approach for the arbitrary size of the block. For the model with three-spin couplings, we calculate the critical point and demonstrate that the phase transition is controlled by an infinite disorder fixed point. We have determined the typical correlation-length critical exponent, which seems to be different from that of the random transverse Ising chain with nearest-neighbor couplings. Thus, this model represents a new infinite disorder universality class. [ABSTRACT FROM AUTHOR]

Collective properties of complex systems composed of many interacting components such as neurons in our brain can be modeled by artificial networks based on disordered systems. We show that a disordered neural network of superconducting loops with Josephson junctions can exhibit computational properties like categorization and associative memory in the time evolution of its state in response to information from external excitations. Superconducting loops can trap multiples of fluxons in many discrete memory configurations defined by the local free energy minima in the configuration space of all possible states. A memory state can be updated by exciting the Josephson junctions to fire or allow the movement of fluxons through the network as the current through them surpasses their critical current thresholds. Simulations performed with a lumped element circuit model of a 4-loop network show that information written through excitations is translated into stable states of trapped flux and their time evolution. Experimental implementation on a high-Tc superconductor YBCO-based 4-loop network shows dynamically stable flux flow in each pathway characterized by the correlations between junction firing statistics. Neural network behavior is observed as energy barriers separating state categories in simulations in response to multiple excitations, and experimentally as junction responses characterizing different flux flow patterns in the network. The state categories that produce these patterns have different temporal stabilities relative to each other and the excitations. This provides strong evidence for time-dependent (short-to-long-term) memories, that are dependent on the geometrical and junction parameters of the loops, as described with a network model. [ABSTRACT FROM AUTHOR]

The pursuit of enhanced superconducting device performance has historically focused on minimizing disorder in materials. Recent research, however, challenges this conventional wisdom by exploring the unique characteristics of disordered materials. Following the studies, disorder is currently viewed as a design parameter that can be tuned. This shift in the paradigm has sparked an upsurge in research efforts, which demonstrates that disorder can significantly augment the superconductivity figures of merit. While almost all previous studies attended to the effects related to disorder strength, this article focuses on the impact of short-range disorder correlations that in real materials takes place, for example, due to lattice defects. The study shows that the degree of such correlations can strongly influence the superconducting characteristics. [ABSTRACT FROM AUTHOR]

This paper focuses on characterizing the energy profile along pathways connecting different regions of configuration space in the context of a prototypical glass model, the pure spherical p -spin model with p = 3. The study investigates pairs of stationary points (local minima or rank-1 saddles), analyzing the energy profile along geodesic paths and comparing them with 'perturbed' pathways correlated to the landscape curvature. The goal is to assess the extent to which information from the local Hessian matrices around stationary points can identify paths with lower energy barriers. Surprisingly, unlike findings in other systems, the direction of softest local curvature is not a reliable predictor of low-energy paths, except in the case in which the direction of softest curvature corresponds to an isolated mode of the Hessian. However, other information encoded in the local Hessian does allow the identification of pathways associated with lower energy barriers. We conclude commenting on implications for the system's activated dynamics. [ABSTRACT FROM AUTHOR]

We derive, within the replica formalism, a generalisation of the Crisanti–Sommers formula to describe the large deviation function (LDF) L (e) for the speed-N atypical fluctuations of the intensive ground-state energy e of a generic spherical spin-glass in the presence of a random external magnetic field of variance Γ . We then analyse our exact formula for the LDF in much detail for the Replica symmetric, single step Replica Symmetry Breaking (1-RSB) and Full Replica Symmetry Breaking (FRSB) situations. Our main qualitative conclusion is that the level of RSB governing the LDF may be different from that for the typical ground-state. We find that while the deepest ground-states are always controlled by a LDF of replica symmetric form, beyond a finite threshold e ≥ e t a replica-symmetry breaking starts to be operative. These findings resolve the puzzling discrepancy between our earlier replica calculations for the p = 2 spherical spin-glass (Fyodorov and Le Doussal in J Stat Phys 154:466, 2014) and the rigorous results by Dembo and Zeitouni (J Stat Phys 159:1306, 2015) which we are able to reproduce invoking an 1-RSB pattern. Finally at an even larger critical energy e c ≥ e t , acting as a "wall", the LDF diverges logarithmically, which we interpret as a change in the large deviation speed from N to a faster growth. In addition, we show that in the limit Γ → 0 the LDF takes non-trivial scaling forms (i) L (e) ∼ G ((e - e c) / Γ) in the vicinity of the wall (ii) L (e) ∼ Γ η ν F ((e - e typ) / Γ ν) in the vicinity of the typical energy, characterised by two new exponents η ≥ 1 and ν characterising universality classes. Via matching the latter allows us to formulate several conjectures concerning the regime of typical fluctuations, identified as e - e typ ∼ N - 1 / η and Γ ∼ N - 1 / (η ν) . [ABSTRACT FROM AUTHOR]

Charge carrier transport via donor/acceptor pairs of similar elements is dominant in n-type MgFe2O4 and p-type Mn3O4 spinels. The temperature-independent activation energy in the form of the nearest neighbor hopping model is applied for Fe2+/Fe3+ pairs of cubic MgFe2O4 spinel in the temperature range of 423–523 K (150–250 °C). At such high temperatures, even for this relatively narrow temperature range, the constant energy barrier deviates to a variable range hopping energy barrier in the case of Mn3O4, due to Jahn-Teller active octahedral sites. Replacing 10 mol% of Fe at octahedral sites with Mn has significantly increased the electron hopping energy barrier and electrical conductivity of MgFe2O4, while keeping the nearest neighbor hopping model dominant. The observed high energy barrier is due to donor/acceptor pairs of different elements (Mn/Fe). Due to a lack of structural distortion, deviation from the nearest neighbor hopping mechanism with temperature-independent activation energy was not observed. Rietveld refined XRD patterns and FT-IR spectra are utilized to support the argument on electrical conductivity mechanisms.

The transmission of a qubit in a tight-binding channel with exponentially decaying hopping terms and diagonal disorder is investigated. The end sites act as sender and receiver and are perturbatively coupled to the channel. This is done to suppress interference of the channel modes during the time evolution of the state. We explore the performance of the transfer fidelity against the disorder strength and hopping range within the channel. The scaling behavior of the participation number as a function of the hopping range is also discussed. Channels featuring long-range interactions display distinct robustness against disorder and high-quality quantum state transfer is attainable even for disorder levels of the order of the largest hopping amplitude. [ABSTRACT FROM AUTHOR]

We consider the disordered monomer-dimer model on cylinder graphs G n , i.e., graphs given by the Cartesian product of the line graph on n vertices, and a deterministic finite graph. The edges carry i.i.d. random weights, and the vertices also have i.i.d. random weights, not necessarily from the same distribution. Given the random weights, we define a Gibbs measure on the space of monomer-dimer configurations on G n . We show that the associated free energy converges to a limit and, with suitable scaling and centering, satisfies a Gaussian central limit theorem. We also show that the number of monomers in a typical configuration satisfies a law of large numbers and a Gaussian central limit theorem with appropriate centering and scaling. Finally, for an appropriate height function associated with a matching, we show convergence to a limiting function and prove the Brownian motion limit around the limiting height function in the sense of finite-dimensional distributional convergence. [ABSTRACT FROM AUTHOR]

There is an ambiguity in how to apply the replica trick to spin glass models which have additional order parameters unrelated to spin glass order—with respect to which quantities does one minimize vs maximize the action, and in what sequence? Here we show that the correct procedure is to first maximize with respect to “replica” order parameters, and then minimize with respect to “conventional” order parameters. With this result, we further elucidate the relationship between quenched free energies, annealed free energies, and replica order—it is possible for the quenched and annealed free energies to differ even while all replica order parameters remain zero. [ABSTRACT FROM AUTHOR]

We present a thorough numerical analysis of the relaxational dynamics of the Sherrington–Kirkpatrick spherical model with an additive non-disordered perturbation for large but finite sizes N. In the thermodynamic limit and at low temperatures, the perturbation is responsible for a phase transition from a spin glass to a ferromagnetic phase. We show that finite-size effects induce the appearance of a distinctive slow regime in the relaxation dynamics, the extension of which depends on the size of the system and also on the strength of the non-disordered perturbation. The long time dynamics are characterized by the two largest eigenvalues of a spike random matrix which defines the model, and particularly by the statistics concerning the gap between them. We characterize the finite-size statistics of the two largest eigenvalues of the spike random matrices in the different regimes, sub-critical, critical, and super-critical, confirming some known results and anticipating others, even in the less studied critical regime. We also numerically characterize the finite-size statistics of the gap, which we hope may encourage analytical work which is lacking. Finally, we compute the finite-size scaling of the long time relaxation of the energy, showing the existence of power laws with exponents that depend on the strength of the non-disordered perturbation in a way that is governed by the finite-size statistics of the gap. [ABSTRACT FROM AUTHOR]

Mechanical metamaterials such as origami or ordered 3D printed structures have shown tremendous applications in science and technology. However, the main disadvantage of these systems is their dependency on a perfectly ordered structure, making them sensitive to defects. Disordered metamaterials offer a way to circumvent this sensitivity. Within disordered metamaterials, crumpled systems have recently received increased attention due to their intriguing properties such as negative Poisson’s ratio, low density, high mechanical shock absorption, and easy manufacturing process. Mechanical relaxation of these systems was successfully explained by stretched exponential and logarithmic models, typically used for complex relaxation in amorphous systems. This drove researchers to study crumpled systems as amorphous systems with a complex energy landscape. Further research remarked similarities between crumpled structures and other metastable systems such as glasses, by studying the mechanical memory effect. Edward’s statistical mechanics was also applied to crumpled systems to unravel their statistical properties. In this review, we summarize different aspects of crumpled materials and their potential to be exploited for designing new robust disordered metamaterials. Finally, we build on the current knowledge and introduce a design principle to make crumpled origami-like structures with robust mechanical responses.

We consider Z -valued p-SOS-models with nearest neighbor interactions of the form | ω v - ω w | p , and finite-spin ferromagnetic models on regular trees. This includes the classical SOS-model, the discrete Gaussian model and the Potts model. We exhibit a family of extremal inhomogeneous (i.e. tree automorphism non-invariant) Gibbs measures arising as low temperature perturbations of ground states (local energy minimizers), which have a sparse enough set of broken bonds together with uniformly bounded increments along them. These low temperature states in general do not possess any symmetries of the tree. This generalises the results of Gandolfo et al. (J. Stat. Phys. 148:999–1005, 2012) about the Ising model, and shows that the latter behaviour is robust. We treat three different types of extensions: non-compact state space gradient models, models without spin-symmetry, and models in small random fields. We give a detailed construction and full proofs of the extremality of the low-temperature states in the set of all Gibbs measures, analysing excess energies relative to the ground states, convergence of low-temperature expansions, and properties of cutsets. [ABSTRACT FROM AUTHOR]

The search for the ferromagnetic quantum critical point (FM QCP) has always been a captivating research topic in the scientific community. In pursuit of this goal, we introduced nonmagnetic transition metals to alloy with elemental nickel, and studied the magnetic properties of nickel binary alloys Ni 1 − x Mo x and Ni 1 − y Cu y as a function of x and y up to the critical concentrations x c r and y c r at which the FM transition T C disappears. T C − x (y) phase diagrams were constructed via the Arrott–Noakes scaling of magnetization data. An enhanced Sommerfeld coefficient (the value of C / T as T → 0) is observed near x c r and y c r , manifesting the effect of quantum fluctuations. However, the spin glass behavior is identified through the ac magnetic susceptibility measurements. This observation rules out the possibility of the existence of the FM QCP in both systems. • Nickel binary alloys Ni 1 − x Mo x with x = 0. 05 − 0. 13 and Ni 1 − y Cu y with y = 0. 20 − 0. 80 synthesized via conventional arc-melting method. • Complete suppression of ferromagnetism is observed near the critical concentrations x c r = 0. 095 and y c r = 0. 54. • x − and y − dependent magnetic critical exponents β , γ , and δ are determined. • Enhanced specific heat coefficients are observed around x c r and y c r due to quantum fluctuations of magnetization. • Spin glass behavior is observed at critical concentrations x c r = 0. 095 in Ni 1 − x Mo x and y c r = 0. 54 in Ni 1 − y Cu y ,. [ABSTRACT FROM AUTHOR]

The model of directed polymer in a random environment is a fundamental model of interaction between a simple random walk and ambient disorder. This interaction gives rise to complex phenomena and transitions from a central limit theory to novel statistical behaviours. Despite its intense study, there are still many aspects and phases which have not yet been identified. In this review we focus on the current status of our understanding of the transition between weak and strong disorder phases, give an account of some of the methods that the study of the model has motivated and highlight some open questions. [ABSTRACT FROM AUTHOR]

The pursuit of enhanced superconducting device performance has historically focused on minimizing disorder in materials. Recent research, however, challenges this conventional wisdom by exploring the unique characteristics of disordered materials. Following the studies, disorder is currently viewed as a design parameter that can be tuned. This shift in the paradigm has sparked an upsurge in research efforts, which demonstrates that disorder can significantly augment the superconductivity figures of merit. While almost all previous studies attended to the effects related to disorder strength, this article focuses on the impact of short-range disorder correlations that in real materials takes place, for example, due to lattice defects. The study shows that the degree of such correlations can strongly influence the superconducting characteristics.

We study the fluctuations of time-additive random observables in the stochastic dynamics of a system of N non-interacting Ising spins. We mainly consider the case of all-to-all dynamics where transitions are possible between any two spin configurations with uniform rates. We show that the cumulant generating function of the time-integral of a normally distributed quenched random function of configurations, i.e. the energy function of the random energy model (REM), has a phase transition in the large N limit for trajectories of any time extent. We prove this by determining the exact limit of the scaled cumulant generating function. This is accomplished by connecting the dynamical problem to a spectral analysis of the all-to-all quantum REM. We also discuss finite N corrections as observed in numerical simulations. This article is part of the theme issue 'Quantum annealing and computation: challenges and perspectives'. [ABSTRACT FROM AUTHOR]

Motivated by the compound LiHoxY1-xF4, we consider the Ising chain with random couplings and in the presence of simultaneous random transverse and longitudinal fields, and study its low-energy properties at zero temperature by the strong disorder renormalization group approach. In the absence of longitudinal fields, the system exhibits a quantum-ordered and a quantum-disordered phase separated by a critical point of infinite disorder. When the longitudinal random field is switched on, the ordered phase vanishes and the trajectories of the renormalization group are attracted to two disordered fixed points: one is characteristic of the classical random field Ising chain, the other describes the quantum disordered phase. The two disordered phases are separated by a separatrix that starts at the infinite disorder fixed point and near which there are strong quantum fluctuations. [ABSTRACT FROM AUTHOR]

Statistical mechanics provides a framework for describing the physics of large, complex many-body systems using only a few macroscopic parameters to determine the state of the system. For isolated quantum many-body systems, such a description is achieved via the eigenstate thermalization hypothesis (ETH), which links thermalization, ergodicity and quantum chaotic behavior. However, tendency towards thermalization is not observed at finite system sizes and evolution times in a robust many-body localization (MBL) regime found numerically and experimentally in the dynamics of interacting many-body systems at strong disorder. Although the phenomenology of the MBL regime is well-established, the central question remains unanswered: under what conditions does the MBL regime give rise to an MBL phase , in which the thermalization does not occur even in the asymptotic limit of infinite system size and evolution time? This review focuses on recent numerical investigations aiming to clarify the status of the MBL phase, and it establishes the critical open questions about the dynamics of disordered many-body systems. The last decades of research have brought an unprecedented new variety of tools and indicators to study the breakdown of ergodicity, ranging from spectral and wave function measures, matrix elements of observables, through quantities probing unitary quantum dynamics, to transport and quantum information measures. We give a comprehensive overview of these approaches and attempt to provide a unified understanding of their main features. We emphasize general trends towards ergodicity with increasing length and time scales, which exclude naive single-parameter scaling hypothesis, necessitate the use of more refined scaling procedures, and prevent unambiguous extrapolations of numerical results to the asymptotic limit. Providing a concise description of numerical methods for studying ETH and MBL, we explore various approaches to tackle the question of the MBL phase. Persistent finite size drifts towards ergodicity consistently emerge in quantities derived from eigenvalues and eigenvectors of disordered many-body systems. The drifts are related to continuous inching towards ergodicity and non-vanishing transport observed in the dynamics of many-body systems, even at strong disorder. These phenomena impede the understanding of microscopic processes at the ETH-MBL crossover. Nevertheless, the abrupt slowdown of dynamics with increasing disorder strength provides premises suggesting the proximity of the MBL phase. This review concludes that the questions about thermalization and its failure in disordered many-body systems remain a captivating area open for further explorations., (Creative Commons Attribution license.)

Copyright of Journal of Xinyang Normal University Natural Science Edition is the property of Journal of Xinyang Normal University Editorial Office and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

We study the problem of assortative and disassortative partitions on random d -regular graphs. Nodes in the graph are partitioned into two non-empty groups. In the assortative partition every node requires at least H of their neighbors to be in their own group. In the disassortative partition they require less than H neighbors to be in their own group. Using the cavity method based on analysis of the belief propagation algorithm we establish for which combinations of parameters (d, H) these partitions exist with high probability and for which they do not. For \lceil \frac{d}{2}\rceil $?> H > ⌈ d 2 ⌉ we establish that the structure of solutions to the assortative partition problems corresponds to the so-called frozen-one-step replica symmetry breaking. This entails a conjecture of algorithmic hardness of finding these partitions efficiently. For H ⩽ ⌈ d 2 ⌉ we argue that the assortative partition problem is algorithmically easy on average for all d. Further we provide arguments about asymptotic equivalence between the assortative partition problem and the disassortative one, going through a close relation to the problem of single-spin-flip-stable states in spin glasses. In the context of spin glasses, our results on algorithmic hardness imply a conjecture that gapped single spin flip stable states are hard to find which may be a universal reason behind the observation that physical dynamics in glassy systems display convergence to marginal stability. [ABSTRACT FROM AUTHOR]

We study the effect of different symmetric random field distributions: trimodal and Gaussian on the phase diagram of the infinite range Blume–Capel model. For the trimodal random field, the model has a very rich phase diagram. We find three new ordered phases, multicritical points like tricritical point (TCP), bicritical end point (BEP), critical end point (CEP) along with some multi-phase coexistence points. We also find re-entrance at low temperatures for some values of the parameters. On the other hand for the Gaussian distribution the phase diagram consists of a continuous line of transition followed by a first order transition line, meeting at a TCP. The TCP vanishes for higher strength of the random field. In contrast to the trimodal case, in Gaussian case no new phase emerges. [ABSTRACT FROM AUTHOR]

Resistivity, ρ (T), and magnetoresistance (MR) are investigated in the Cu2Zn1âˆ' x Cd x SnS4 single crystals for compositions x ≡ Cd/(Zn + Cd) = 0.15â€"0.24, in the temperature range of T ∼ 50â€"300 K in pulsed magnetic fields of B up to 20 T. The Mott variable-range hopping (VRH) conductivity is established within wide temperature intervals lying inside Î" T M ∼ 60â€"190 K for different x. The deviations from the VRH conduction, observable above and below Î" T M, are connected to the nearest-neighbor hopping regime and to the activation on the mobility threshold of the acceptor band (AB) with width W ≈ 16â€"46 meV. The joint analysis of ρ (T) and positive MR permitted determination of other important electronic parameters. These include the localization radius, α ≈ 19â€"30 Ă..., the density of the localized states, g (ÎĽ) ≈ (1.6â€"21) Ă— 1017 meVâˆ'1 cmâˆ'3 at the Fermi level ÎĽ, and the acceptor concentration, N A ∼ (6â€"8) Ă— 1019 cmâˆ'3, for various x and in conditions of different vicinity of the investigated samples to the metalâ€"insulator transition. In addition, details of the AB structure, including positions of ÎĽ and of the mobility threshold, E c, are found depending on the alloy composition. [ABSTRACT FROM AUTHOR]

Gradient descent dynamics in complex energy landscapes, i.e. featuring multiple minima, finds application in many different problems, from soft matter to machine learning. Here, we analyze one of the simplest examples, namely that of soft repulsive particles in the limit of infinite spatial dimension d. The gradient descent dynamics then displays a jamming transition: at low density, it reaches zero-energy states in which particles’ overlaps are fully eliminated, while at high density the energy remains finite and overlaps persist. At the transition, the dynamics becomes critical. In the d â†' ∞ limit, a set of self-consistent dynamical equations can be derived via mean field theory. We analyze these equations and we present some partial progress towards their solution. We also study the random Lorentz gas in a range of d = 2…22, and obtain a robust estimate for the jamming transition in d â†' ∞. The jamming transition is analogous to the capacity transition in supervised learning, and in the appendix we discuss this analogy in the case of a simple one-layer fully-connected perceptron. [ABSTRACT FROM AUTHOR]

Resistance ρ of an one-dimensional disordered system of length L has the log-normal distribution in the limit of large L. Parameters of this distribution depend on the Fermi level position, but are independent on the boundary conditions. However, the boundary conditions essentially affect the distribution of phases entering the transfer matrix and generally change the parameters of the evolution equation for the distribution P (ρ). This visible contradiction is resolved by the existence of the hidden symmetry, whose nature is revealed by the derivation of the equation for the stationary phase distribution and by analysis of its transformation properties. [ABSTRACT FROM AUTHOR]

Asymmetry in the synaptic interactions between neurons plays a crucial role in determining the memory storage and retrieval properties of recurrent neural networks. In this work, we analyze the problem of storing random memories in a network of neurons connected by a synaptic matrix with a definite degree of asymmetry. We study the corresponding satisfiability and clustering transitions in the space of solutions of the constraint satisfaction problem associated with finding synaptic matrices given the memories. We find, besides the usual SAT/UNSAT transition at a critical number of memories to store in the network, an additional transition for very asymmetric matrices, where the competing constraints (definite asymmetry vs memories storage) induce enough frustration in the problem to make it impossible to solve. This finding is particularly striking in the case of a single memory to store, where no quenched disorder is present in the system. [ABSTRACT FROM AUTHOR]

We consider the dynamics of the quantum XY chain with disorder under thegeneral assumption that the expectation of the eigenfunction correlator of theassociated one-particle Hamiltonian satisfies a decay estimate typical ofAnderson localization. We show that, starting from a broad class of productinitial states, entanglement remains bounded for all times. For the XX chain,we also derive bounds on the particle transport which, in particular, show thatthe density profile of initial states that consist of fully occupied and emptyintervals, only have significant dynamics near the edges of those intervals,uniformly for all times.

Complex systems can be characterized by their level of order or disorder. An ordered system is related to the presence of system properties that are correlated with each other. For example, it has been found in crisis periods that the financial systems tend to be synchronized, and symmetry appears in financial assets' behavior. In retail, the collective purchasing behavior tends to be highly disorderly, with a diversity of correlation patterns appearing between the available market supply. In those cases, it is essential to understand the hierarchical structures underlying these systems. For the latter, community detection techniques have been developed to find similar behavior clusters according to some similarity measure. However, these techniques do not consider the inherent interactions between the multitude of system elements. This paper proposes and tests an approach that incorporates a hierarchical grouping process capable of dealing with complete weighted networks. Experiments show that the proposal is superior in terms of the ability to find minimal energy clusters. These minimum energy clusters are equivalent to system states (market baskets) with a higher probability of occurrence; therefore, they are interesting for marketing and promotion activities in retail environments.

The mechanism of high harmonic generation (HHG) from condensed matter driven by ultrafast lasers is far from being understood due to the structural diversity and complexity. One of the long-standing open questions is the effect of random disorder in noncrystal HHG. In this work, we identify the critical role of correlations in disordered semiconductor systems and propose them as the criterion to classify the HHG processes. The HHG spectra can be classified into two different categories corresponding to different correlations: short-range correlation and long-range correlation (LRC). Thus correlations build up a solid relationship between the HHG emission and statistical characteristics of a disordered system. In particular, the HHG spectrum from the disordered system with LRC exhibits remarkable consistency with the spectrum from the periodic lattice, revealing that the LRC links HHG processes in disordered and periodic systems. Besides, the mobility edge induced by the long-range correlated disorder enables us to study the behavior of localized- and delocalized-state HHG in one system. [ABSTRACT FROM AUTHOR]

Multifunctional composite nanosystems containing both one-dimensional and two-dimensional nanostructures possess improved electrical, mechanical, and thermal properties which offer a wide range of applications. In this work, the composite films formed by single-walled carbon nanotubes and MoS2 flakes (MoS2-SWNTs) are studied exploiting Raman spectroscopy, scanning electron microscopy, and low-temperature conductivity measurements (5–312 K). The MoS2-SWNTs and SWNTs films demonstrate the semiconductor behavior with negative temperature coefficient of resistance. The temperature dependence of the composite film resistance in the range of 5–204 K is considered whithin the framework of Mott model that describes the motion of electrons with variable range hopping due to thermally activated tunneling (3D Mott VRH model). At T > 204 K, the temperature dependence of composite film resistance was fitted by the Arrhenius-like equation. The empirical parameters included in two transport models were evaluated. The comparison between the composite and SWNTs films shows that the conductivity of the composite is mostly determined by nanotubes. [ABSTRACT FROM AUTHOR]

We use large deviation theory to obtain the free energy of the XY model on a fully connected graph on each site of which there is a randomly oriented field of magnitude h. The phase diagram is obtained for two symmetric distributions of the random orientations: (a) a uniform distribution and (b) a distribution with cubic symmetry. In both cases, the disorderâ€"averaged ordered state reflects the symmetry of the underlying distribution. The phase boundary has a multicritical point (MCP) which separates a locus of continuous transitions (for small values of h) from a locus of first order transitions (for large h). The free energy is a function of a single variable in case (a) and a function of two variables in case (b), leading to different characters of the MCPs in the two cases. We find that the locus of continuous transitions is given by the same equation for a family of quadriperiodic distributions, which includes the distributions (a) and (b). However, the location of the MCP and the nature of ordered state depend on the form of the distribution. The disorder-averaged ground state energy is found exactly, and the specific heat is shown to approach a constant as temperature approaches zero. [ABSTRACT FROM AUTHOR]

The diffuse scattering signal of amorphous or liquid systems contains information on the local atomic structure, and this can be related to the density, compressibility, thermal expansion and other thermoelastic properties. However, the analysis and full exploitation of the diffuse scattering signal, in particular for systems under extreme conditions of high pressures and temperatures are difficult to handle. Amorpheus is a Python-based software allowing the determination of the structure factor and the radial distribution function of amorphous and liquid systems. Based on previously reported methodologies, Amorpheus stands out for the implementation of automatic algorithms allowing the user to choose the most suitable parameters for the data treatment and making possible systematic analysis of datasets collected in experiments carried out in Paris-Edinburgh press, multi-anvil apparatus or diamond anvil cell. [ABSTRACT FROM AUTHOR]

Motivated by recent advances on local conductance measurement techniques at the nanoscale, timely questions are being raised about what possible information can be extracted from a disordered graphene sheet by selectively interrogating its transport properties. Here we demonstrate how an inversion technique originally developed to identify the number of scatterers in a quantum device can be adapted to a multi-terminal setup in order to provide detailed information about the spatial distribution of impurities on the surface of graphene, as well as other 2D material systems. The methodology input are conductance readings (for instance, as a function of the chemical potential) between different electrode pairs, the output being the spatially resolved impurity density. We discuss how the obtained spatial resolution depends on the number of such readings and on the electrode geometry. Furthermore, by separating the impurity locations into partitions arranged in a grid-like geometry, this inversion procedure resembles a Sudoku puzzle in which the compositions of different sectors of a device are found by imposing that they must add up to specific constrained values established for the grid rows and columns. We argue that this technique may provide alternative new ways of extracting information from a disordered material through the selective probing of local quantities. [Display omitted] [ABSTRACT FROM AUTHOR]

Topological materials with Dirac electron systems have been extensively studied. Organic crystalline materials form a unique group of such compounds with well-defined crystal structures. While most organic compounds require high pressures to exhibit Dirac-cone-type band structures, the title compound, α-STF2I3, has garnered increasing interest due to its Dirac-cone-type band structure under ambient pressure. Various experiments have been conducted under ambient pressure; their results can be compared with those of theoretical calculations to obtain insights into Dirac electron systems. However, structural disorder peculiar to the STF molecules in the solid-state has prevented any type of theoretical calculation of the states. In this study, we report a new method for calculating intermolecular interactions in disordered systems based on the extended Hückel approximation. This method enables band calculations, suggesting that this material is a rare example of a system close to merging. The obtained band structure indicates that the characteristic disorder in the STF solids distributed electrons equally on the sulphur and selenium atoms as if they belong to an imaginary element between sulphur and selenium and are arranged without disorder. [ABSTRACT FROM AUTHOR]

We find the free-energy in the thermodynamic limit of a one-dimensional XY model associated to a system of N qubits. The coupling among the σ i z is a long range two-body random interaction. The randomness in the couplings is the typical interaction of the Hopfield model with p patterns ( p < N ), where the patterns are p sequences of N independent identically distributed random variables (i.i.d.r.v.), assuming values ± 1 with probability 1 / 2 . We show also that in the case p ≤ α N , α ≠ 0 , the free-energy is asymptotically independent from the choice of the patterns, i.e., it is self-averaging.

We observe the failure process of a fiber bundle model with a variable stress release range, γ, and higher the value of γ, lower the stress release range. By tuning γ from low to high, it is possible to go from the mean-field (MF) limit of the model to the local load-sharing (LLS) limit where local stress concentration plays a crucial role. In the MF limit, individual avalanches (number of fibers breaking in going from one stable state to the next, s) and the corresponding energies E emitted during those avalanches have one-to-one linear correlation. This results in the same size distributions for both avalanches (P(s)) and energy bursts (Q(E)): a scale-free distribution with a universal exponent value of −5/2. With increasing γ, the model enters the LLS limit beyond some γc. In this limit, due to the presence of local stress concentrations around a damaged region, such correlation C(γ) between s and E decreases, i.e., a smaller avalanche can emit a large amount of energy or a large avalanche may emit a small amount of energy. The nature of the decrease in the correlation between s and E depends highly on the dimension of the bundle. In this work, we study the decrease in the correlation between avalanche size and the corresponding energy bursts with an increase in the load redistribution localization in the fiber bundle model in one and two dimensions. Additionally, we note that the energy size distribution remains scale-free for all values of γ, whereas the avalanche size distribution becomes exponential for γ > γc.