SEARCH · Searcharxiv

Results for “cond-mat.dis-nn”

Search indexed arXiv papers on artificial intelligence, large language models, computer vision and robotics. Read source abstracts and follow links to arXiv.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 253 records · Page 14Linked to original sources

arXiv2013

Complex Network Structure of Flocks in the Standard Vicsek Model

In flocking models, the collective motion of self-driven individuals leads to the formation of complex spatiotemporal patterns. The Standard Vicsek Model (SVM) considers individuals that tend to adopt the direction of movement of their neighbors under the influence of noise. By performing an extensive complex network characterization of the structure of SVM flocks, we show that flocks are highly clustered, assortative, and non-hierarchical networks with short-tailed degree distributions. Moreover, we also find that the SVM dynamics leads to the formation of complex structures with an effective dimension higher than that of the space where the actual displacements take place. Furthermore, we show that these structures are capable of sustaining mean-field-like orientationally ordered states when the displacements are suppressed, thus suggesting a linkage between the onset of order and the enhanced dimensionality of SVM flocks.

cond-mat.stat-mech↗

arXiv2013

Topology trivialization and large deviations for the minimum in the simplest random optimization

Finding the global minimum of a cost function given by the sum of a quadratic and a linear form in N real variables over (N-1)- dimensional sphere is one of the simplest, yet paradigmatic problems in Optimization Theory known as the "trust region subproblem" or "constraint least square problem". When both terms in the cost function are random this amounts to studying the ground state energy of the simplest spherical spin glass in a random magnetic field. We first identify and study two distinct large-N scaling regimes in which the linear term (magnetic field) leads to a gradual topology trivialization, i.e. reduction in the total number N_{tot} of critical (stationary) points in the cost function landscape. In the first regime N_{tot} remains of the order $N$ and the cost function (energy) has generically two almost degenerate minima with the Tracy-Widom (TW) statistics. In the second regime the number of critical points is of the order of unity with a finite probability for a single minimum. In that case the mean total number of extrema (minima and maxima) of the cost function is given by the Laplace transform of the TW density, and the distribution of the global minimum energy is expected to take a universal scaling form generalizing the TW law. Though the full form of that distribution is not yet known to us, one of its far tails can be inferred from the large deviation theory for the global minimum. In the rest of the paper we show how to use the replica method to obtain the probability density of the minimum energy in the large-deviation approximation by finding both the rate function and the leading pre-exponential factor.

cond-mat.dis-nn↗

arXiv2014

Survival of classical and quantum particles in the presence of traps

We present a detailed comparison of the motion of a classical and of a quantum particle in the presence of trapping sites, within the framework of continuous-time classical and quantum random walk. The main emphasis is on the qualitative differences in the temporal behavior of the survival probabilities of both kinds of particles. As a general rule, static traps are far less efficient to absorb quantum particles than classical ones. Several lattice geometries are successively considered: an infinite chain with a single trap, a finite ring with a single trap, a finite ring with several traps, and an infinite chain and a higher-dimensional lattice with a random distribution of traps with a given density. For the latter disordered systems, the classical and the quantum survival probabilities obey a stretched exponential asymptotic decay, albeit with different exponents. These results confirm earlier predictions, and the corresponding amplitudes are evaluated. In the one-dimensional geometry of the infinite chain, we obtain a full analytical prediction for the amplitude of the quantum problem, including its dependence on the trap density and strength.

cond-mat.stat-mech↗

arXiv2014

The network source location problem: ground state energy, entropy and effects of freezing

Ground state entropy of the network source location problem is evaluated at both the replica symmetric level and one-step replica symmetry breaking level using the entropic cavity method. The regime that is a focus of this study, is closely related to the vertex cover problem with randomly quenched covered nodes. The resulting entropic message passing inspired decimation and reinforcement algorithms are used to identify the optimal location of sources in single instances of transportation networks. The conventional belief propagation without taking the entropic effect into account is also compared. We find that in the glassy phase the entropic message passing inspired decimation yields a lower ground state energy compared to the belief propagation without taking the entropic effect. Using the extremal optimization algorithm, we study the ground state energy and the fraction of frozen hubs, and extend the algorithm to collect statistics of the entropy. The theoretical results are compared with the extremal optimization results.

cond-mat.dis-nn↗

arXiv2018

Non-Convex Multi-species Hopfield models

In this work we introduce a multi-species generalization of the Hopfield model for associative memory, where neurons are divided into groups and both inter-groups and intra-groups pair-wise interactions are considered, with different intensities. Thus, this system contains two of the main ingredients of modern Deep neural network architectures: Hebbian interactions to store patterns of information and multiple layers coding different levels of correlations. The model is completely solvable in the low-load regime with a suitable generalization of the Hamilton-Jacobi technique, despite the Hamiltonian can be a non-definite quadratic form of the magnetizations. The family of multi-species Hopfield model includes, as special cases, the 3-layers Restricted Boltzmann Machine (RBM) with Gaussian hidden layer and the Bidirectional Associative Memory (BAM) model.

cond-mat.dis-nn↗

arXiv2013

Localization of disordered bosons and magnets in random fields

We study localization properties of disordered bosons and spins in random fields at zero temperature. We focus on two representatives of different symmetry classes, hard-core bosons (XY magnets) and Ising magnets in random transverse fields, and contrast their physical properties. We describe localization properties using a locator expansion on general lattices. For 1d Ising chains, we find non-analytic behavior of the localization length as a function of energy at ω= 0, $ξ^{-1}(ω) = ξ^{-1}(0) + A |ω|^α$, with $α$ vanishing at criticality. This contrasts with the much smoother behavior predicted for XY magnets. We use these results to approach the ordering transition on Bethe lattices of large connectivity K, which mimic the limit of high dimensionality. In both models, in the paramagnetic phase with uniform disorder, the localization length is found to have a local maximum at ω= 0. For the Ising model, we find activated scaling at the phase transition, in agreement with infinite randomness studies. In the Ising model long range order is found to arise due to a delocalization and condensation initiated at ω= 0, without a closing mobility gap. We find that Ising systems establish order on much sparser (fractal) subgraphs than XY models. Possible implications of these results for finite-dimensional systems are discussed.

cond-mat.dis-nn↗

arXiv2012

Low Depth Quantum Circuits for Ising Models

A scheme for measuring complex temperature partition functions of Ising models is introduced. In the context of ordered qubit registers this scheme finds a natural translation in terms of global operations, and single particle measurements on the edge of the array. Two applications of this scheme are presented. First, through appropriate Wick rotations, those amplitudes can be analytically continued to yield estimates for partition functions of Ising models. Bounds on the estimation error, valid with high confidence, are provided through a central-limit theorem, which validity extends beyond the present context. It holds for example for estimations of the Jones polynomial. Interestingly, the kind of state preparations and measurements involved in this application can in principle be made "instantaneous", i.e. independent of the system size or the parameters being simulated. Second, the scheme allows to accurately estimate some non-trivial invariants of links. A third result concerns the computational power of estimations of partition functions for real temperature classical ferromagnetic Ising models on a square lattice. We provide conditions under which estimating such partition functions allows one to reconstruct scattering amplitudes of quantum circuits making the problem BQP-hard. Using this mapping, we show that fidelity overlaps for ground states of quantum Hamiltonians, which serve as a witness to quantum phase transitions, can be estimated from classical Ising model partition functions. Finally, we show that the ability to accurately measure corner magnetizations on thermal states of two-dimensional Ising models with magnetic field leads to fully polynomial random approximation schemes (FPRAS) for the partition function. Each of these results corresponds to a section of the text that can be essentially read independently.

quant-ph↗

arXiv2018

Slow relaxation dynamics in binary glasses during stress-controlled, tension-compression cyclic loading

The effect of cyclic loading on relaxation dynamics and mechanical properties of metallic glasses is studied using molecular dynamics simulations. We consider the Kob-Andersen three-dimensional binary mixture rapidly cooled across the glass transition and subjected to thousands of tension-compression cycles in the elastic range. It was found that during cyclic loading at constant pressure, the system is relocated to progressively lower levels of the potential energy, thus promoting greater densification and higher strength. Furthermore, with increasing stress amplitude, the average glass density increases and the minimum of the potential energy becomes deeper, while the elastic modulus is reduced. The typical size of clusters of atoms with large nonaffine displacements becomes smaller over consecutive cycles, which correlates with the gradual decrease in the potential energy. These results are important for thermomechanical processing of metallic glasses with improved mechanical properties.

cond-mat.soft↗

arXiv2013

Numerical Approaches on Driven Elastic Interfaces in Random Media

We discuss the universal dynamics of elastic interfaces in quenched random media. We focus in the relation between the rough geometry and collective transport properties in driven steady-states. Specially devised numerical algorithms allow us to analyze the equilibrium, creep, and depinning regimes of motion in minimal models. The relevance of our results for understanding domain wall experiments is outlined.

cond-mat.dis-nn↗

arXiv2021

Role of Frustration in a Weakly Disordered Checkerboard Lattice

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.

cond-mat.dis-nn↗

arXiv2013

Quantum Annealing for Dirichlet Process Mixture Models with Applications to Network Clustering

We developed a new quantum annealing (QA) algorithm for Dirichlet process mixture (DPM) models based on the Chinese restaurant process (CRP). QA is a parallelized extension of simulated annealing (SA), i.e., it is a parallel stochastic optimization technique. Existing approaches [Kurihara et al. UAI2009, Sato et al. UAI2009] and cannot be applied to the CRP because their QA framework is formulated using a fixed number of mixture components. The proposed QA algorithm can handle an unfixed number of classes in mixture models. We applied QA to a DPM model for clustering vertices in a network where a CRP seating arrangement indicates a network partition. A multi core processor was used for running QA in experiments, the results of which show that QA is better than SA, Markov chain Monte Carlo inference, and beam search at finding a maximum a posteriori estimation of a seating arrangement in the CRP. Since our QA algorithm is as easy as to implement the SA algorithm, it is suitable for a wide range of applications.

cond-mat.dis-nn↗

arXiv2013

Universality, exponents and anomaly cancellation in disordered Dirac fermions

Disordered 2D chiral fermions provide an effective description of several materials including graphene and topological insulators. While previous analysis considered delta correlated disorder and no ultraviolet cut-offs, we consider here the effect of short range correlated disorder and the presence of a momentum cut-off, providing a more realistic description of condensed matter models. We show that the density of states is anomalous with a critical exponent function of the disorder and that conductivity is universal only when the ultraviolet cut-off is removed, as consequence of the supersymmetric cancellation of the anomalies.

cond-mat.dis-nn↗

arXiv2014

Market structure explained by pairwise interactions

Financial markets are a typical example of complex systems where interactions between constituents lead to many remarkable features. Here, we show that a pairwise maximum entropy model (or auto-logistic model) is able to describe switches between ordered (strongly correlated) and disordered market states. In this framework, the influence matrix may be thought as a dissimilarity measure and we explain how it can be used to study market structure. We make the link with the graph-theoretic description of stock markets reproducing the non-random and scale-free topology, shrinking length during crashes and meaningful clustering features as expected. The pairwise model provides an alternative method to study financial networks which may be useful for characterization of abnormal market states (crises and bubbles), in capital allocation or for the design of regulation rules.

q-fin.ST↗

arXiv2014

Theory of dipolaron solutions

A fundamental task of statistical physics is to predict the system's statistical properties and compare them with observable data. We formulate the theory of dipolaron solutions and analyze the screening effects for permanent and field-induced dipolarons. The mathematical treatment of the collective behaviour and microscopical morphology of dipolaron solutions are discussed. The presented computations show that the electric field shielding of dipolarons in dielectric nanosolutions is quite different from that of counterionic nano-complexes of Debye-Hückel theory of electrolytes. The limiting case of screening length $λ=0$ in dipolaron solutions corresponds to Coulomb's law for the potential and field of uniformly charged sphere.

cond-mat.stat-mech↗

arXiv2022

Bias induced drift and trapping on random combs and the Bethe lattice: Fluctuation regime and first order phase transitions

We study the competition between field-induced transport and trapping in a disordered medium by studying biased random walks on random combs and the bond-diluted Bethe lattice above the percolation threshold. While it is known that the drift velocity vanishes above a critical threshold, here our focus is on fluctuations, characterized by the variance of the transit times. On the random comb, the variance is calculated exactly for a given realization of disorder using a 'forward transport' limit which prohibits backward movement along the backbone but allows an arbitrary number of excursions into random-length branches. The disorder-averaged variance diverges at an earlier threshold of the bias, implying a regime of anomalous fluctuations, although the velocity is nonzero. Our results are verified numerically using a Monte Carlo procedure that is adapted to account for ultra-slow returns from long branches. On the Bethe lattice, we derive an upper bound for the critical threshold bias for anomalous fluctuations of the mean transit time averaged over disorder realizations. Finally, as for the passage to the vanishing velocity regime, it is shown that the transition to the anomalous fluctuation regime can change from continuous to first order depending on the distribution of branch lengths.

cond-mat.stat-mech↗

arXiv2013

Anderson localization in a two-dimensional random gap model

We study the properties of the spinor wavefunction in a strongly disordered environment on a two-dimensional lattice. By employing a transfer-matrix calculation we find that there is a transition from delocalized to localized states at a critical value of the disorder strength. We prove that there exists an Anderson localized phase with exponentially decaying correlations for sufficiently strong scattering. Our results indicate that suppressed backscattering is not sufficient to prevent Anderson localization of surface states in topological insulators.

cond-mat.dis-nn↗

arXiv2014

Absolutely continuous energy bands in the electronic spectrum of quasiperiodic ladder networks

The energy spectra of quasi-one dimensional quasiperiodic ladder networks are analyzed within a tight binding description. In particular, we show that if a selected set of sites in each strand of a ladder is tunnel-coupled to quantum dots attached from a side, absolutely continuous subbands can be generated in the spectrum if one tunes the dot potential and the dot-strand coupling appropriately. Typical cases with two and three strand Fibonacci ladders in the off diagonal model are discussed in details. We also discuss the possibility of re-entrant insulator-metal transition for a general n-strand ladder network when n becomes large. The observations remain valid even in the case of a disordered ladder network with the same constituents. The results are analytically exact.

cond-mat.dis-nn↗

arXiv2013

Strange Attractor in the Potts Spin Glass on Hierarchical Lattices

The spin-glass $q$-state Potts model on $d$-dimensional diamond hierarchical lattices is investigated by an exact real space renormalization group scheme. Above a critical dimension $d_l(q)$ for $q > 2$, the coupling constants probability distribution flows to a low-temperature \emph{strange attractor} or to the high-temperature paramagnetic fixed point, according to the temperature is below or above the critical temperature $T_c(q,d)$. The strange attractor was investigated considering four initial different distributions for $q = 3$ and $d = 5$ presenting strong robustness in shape and temperature interval suggesting a condensed phase with algebraic decay.

cond-mat.dis-nn↗