6
6.0
Jun 26, 2018
06/18
by
Zhi-Yuan Sun; Shmuel Fishman; Avy Soffer
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Dynamics of solitons of the Ablowitz-Ladik model in the presence of a random potential is studied. In absence of the random potential it is an integrable model and the solitons are stable. As a result of the random potential this stability is destroyed. In some regime, for short times particle-like dynamics with constant mass is found. There is another regime, where particle-like dynamics with varying mass takes place. In particular an effective potential is found. It predicts correctly changes...
Topics: Disordered Systems and Neural Networks, Condensed Matter
Source: http://arxiv.org/abs/1501.04231
9
9.0
Jun 28, 2018
06/18
by
Václav Janiš
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We discuss the mean-field theory of spin-glass models with frustrated long-range random spin exchange. We analyze the reasons for breakdown of the simple mean-field theory of Sherrington and Kirkpatrick. We relate the replica-symmetry breaking to ergodicity breaking and use the concept of real replicas to restore thermodynamic homogeneity of the equilibrium free energy in a replicated phase space. Embedded replications of the spin variables result in a set of hierarchical free energies and...
Topics: Disordered Systems and Neural Networks, Condensed Matter
Source: http://arxiv.org/abs/1506.07128
2
2.0
Jun 29, 2018
06/18
by
Malte Schröder; Wei Chen; Jan Nagler
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Recently it has been demonstrated that the connectivity transition from microscopic connectivity to macroscopic connectedness, known as percolation, is generically announced by a cascade of microtransitions of the percolation order parameter [Chen et al., Phys. Rev. Lett. 112, 155701 (2014)]. Here we report the discovery of macrotransition cascades which follow percolation. The order parameter grows in discrete macroscopic steps with positions that can be randomly distributed even in the...
Topics: Disordered Systems and Neural Networks, Condensed Matter
Source: http://arxiv.org/abs/1601.05996
4
4.0
Jun 29, 2018
06/18
by
H. Hatami; C. Danieli; J. D. Bodyfelt; S. Flach
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We consider a quantum particle in a one-dimensional disordered lattice with Anderson localization, in the presence of multi-frequency perturbations of the onsite energies. Using the Floquet representation, we transform the eigenvalue problem into a Wannier-Stark basis. Each frequency component contributes either to a single channel or a multi-channel connectivity along the lattice, depending on the control parameters. The single channel regime is essentially equivalent to the undriven case. The...
Topics: Disordered Systems and Neural Networks, Condensed Matter
Source: http://arxiv.org/abs/1602.02476
2
2.0
Jun 29, 2018
06/18
by
Cyril Furtlehner; Aurélien Decelle
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We elaborate on the idea that loop corrections to belief propagation could be dealt with in a systematic way on pairwise Markov random fields, by using the elements of a cycle basis to define region in a generalized belief propagation setting. The region graph is specified in such a way as to avoid dual loops as much as possible, by discarding redundant Lagrange multipliers, in order to facilitate the convergence, while avoiding instabilities associated to minimal factor graph construction. We...
Topics: Disordered Systems and Neural Networks, Condensed Matter
Source: http://arxiv.org/abs/1602.03102
8
8.0
Jun 26, 2018
06/18
by
Patrick Charbonneau; Yuliang Jin; Giorgio Parisi; Corrado Rainone; Beatriz Seoane; Francesco Zamponi
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Recent theoretical advances predict the existence, deep into the glass phase, of a novel phase transition, the so-called Gardner transition. This transition is associated with the emergence of a complex free energy landscape composed of many marginally stable sub-basins within a glass metabasin. In this study, we explore several methods to detect numerically the Gardner transition in a simple structural glass former, the infinite-range Mari-Kurchan model. The transition point is robustly...
Topics: Disordered Systems and Neural Networks, Condensed Matter
Source: http://arxiv.org/abs/1501.07244
3
3.0
Jun 30, 2018
06/18
by
Itamar Procaccia; Corrado Rainone; Murari Singh
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eye 3
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The mechanical failure of amorphous media is a ubiquitous phenomenon from material engineering to geology. It has been noticed for a long time that the phenomenon is "scale-free", indicating some type of criticality. In spite of attempts to invoke "Self-Organized Criticality", the physical origin of this criticality, and also its universal nature, being quite insensitive to the nature of microscopic interactions, remained elusive. Recently we proposed that the precise nature...
Topics: Disordered Systems and Neural Networks, Condensed Matter
Source: http://arxiv.org/abs/1704.05285
3
3.0
Jun 30, 2018
06/18
by
Kabir Ramola; Christophe Texier
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We study the fluctuations of certain random matrix products $\Pi_N=M_N\cdots M_2M_1$ of $\mathrm{SL}(2,\mathbb{R})$, describing localisation properties of the one-dimensional Dirac equation with random mass. In the continuum limit, i.e. when matrices $M_n$'s are close to the identity matrix, we obtain convenient integral representations for the variance $\Gamma_2=\lim_{N\to\infty}\mathrm{Var}(\ln||\Pi_N||)/N$. The case studied exhibits a saturation of the variance at low energy $\varepsilon$...
Topics: Disordered Systems and Neural Networks, Condensed Matter
Source: http://arxiv.org/abs/1402.6943
4
4.0
Jun 30, 2018
06/18
by
Juntao Song; Emil Prodan
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eye 4
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Using an explicit 1-dimensional model, we provide direct evidence that the one-dimensional topological phases from the AIII and BDI symmetry classes follow a $\mathbb Z$-classification, even in the strong disorder regime when the Fermi level is embedded in a dense localized spectrum. The main tool for our analysis is the winding number $\nu$, in the non-commutative formulation introduced in I. Mondragon-Shem, J. Song, T. L. Hughes, and E. Prodan, arXiv:1311.5233. For both classes, by varying...
Topics: Disordered Systems and Neural Networks, Condensed Matter
Source: http://arxiv.org/abs/1402.7116
2
2.0
Jun 29, 2018
06/18
by
Yang Wei Koh
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eye 2
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We present an extensive numerical study of the Sherrington-Kirkpatrick model in transverse field. Recent numerical studies of quantum spin-glasses have focused on exact diagonalization of the full Hamiltonian for small systems ($\approx$ 20 spins). However, such exact numerical treatments are difficult to apply on larger systems. We propose making an approximation by using only a subspace of the full Hilbert space spanned by low-lying excitations consisting of one-spin flipped and two-spin...
Topics: Disordered Systems and Neural Networks, Condensed Matter
Source: http://arxiv.org/abs/1604.01145
2
2.0
Jun 29, 2018
06/18
by
A. V. Syromyatnikov; A. V. Sizanov
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We discuss magnetically ordered ("superfluid") phase near quantum transition to Bose-glass phase in a simple modeling system, Heisenberg antiferromagnet in spatial dimension $d>2$ in external magnetic field with disorder in exchange coupling constants. Our analytical consideration is based on hydrodynamic description of long-wavelength excitations. Results obtained are valid in the entire critical region near the quantum critical point (QCP) allowing to describe a possible...
Topics: Disordered Systems and Neural Networks, Condensed Matter
Source: http://arxiv.org/abs/1604.08728
2
2.0
Jun 29, 2018
06/18
by
Shunsuke Watanabe; Yoshiyuki Kabashima
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In this study, we investigate the resilience of duplex networked layers ($\alpha$ and $\beta$) coupled with antagonistic interlinks, each layer of which inhibits its counterpart at the microscopic level, changing the following factors: whether the influence of the initial failures in $\alpha$ remains (quenched (Case Q)) or not (free (Case F)); the effect of intralayer degree-degree correlations in each layer and interlayer degree-degree correlations; and the type of the initial failures, such...
Topics: Disordered Systems and Neural Networks, Condensed Matter
Source: http://arxiv.org/abs/1605.05442
3
3.0
Jun 29, 2018
06/18
by
Agnieszka Werpachowska
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eye 3
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The Comment to the Letter "Excitons in Molecular Aggregates with Levy Disorder: Anomalous Localization and Exchange Broadening of Optical Spectra" appeared in Phys. Rev. Lett. 109, 259701 (submitted on November 28, 2011). I prepared the below response to the rebuttal received from the Letter's Authors in the review process. It contains useful comments, which further address the errors in the Letter and other flaws in Authors' understanding of the topic revealed in discussion.
Topics: Disordered Systems and Neural Networks, Condensed Matter
Source: http://arxiv.org/abs/1606.01820
2
2.0
Jun 29, 2018
06/18
by
Maycon S. Araújo; André P. Vieira; José S. Andrade; Hans J. Herrmann
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We investigate a model for fatigue crack growth in which damage accumulation is assumed to follow a power law of the local stress amplitude, a form which can be generically justified on the grounds of the approximately self-similar aspect of microcrack distributions. Our aim is to determine the relation between model ingredients and the Paris exponent governing subcritical crack-growth dynamics at the macroscopic scale, starting from a single small notch propagating along a fixed line. By a...
Topics: Disordered Systems and Neural Networks, Condensed Matter
Source: http://arxiv.org/abs/1608.02613
3
3.0
Jun 30, 2018
06/18
by
Gino Del Ferraro; Chuang Wang; Dani Martí; Marc Mézard
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In this three-sections lecture cavity method is introduced as heuristic framework from a Physics perspective to solve probabilistic graphical models and it is presented both at the replica symmetric (RS) and 1-step replica symmetry breaking (1RSB) level. This technique has been applied with success on a wide range of models and problems such as spin glasses, random constrain satisfaction problems (rCSP), error correcting codes etc. Firstly, the RS cavity solution for Sherrington-Kirkpatrick...
Topics: Disordered Systems and Neural Networks, Condensed Matter
Source: http://arxiv.org/abs/1409.3048
3
3.0
Jun 30, 2018
06/18
by
Bernard Derrida; Peter Mottishaw
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eye 3
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We present a systematic and exact way of computing finite size corrections for the random energy model, in its low temperature phase. We obtain explicit (though complicated) expressions for the finite size corrections of the overlap functions. In its low temperature phase, the random energy model is known to exhibit Parisi's broken symmetry of replicas. The finite size corrections given by our exact calculation can be reproduced using replicas if we make specific assumptions about the...
Topics: Disordered Systems and Neural Networks, Condensed Matter
Source: http://arxiv.org/abs/1410.1432
5
5.0
Jun 27, 2018
06/18
by
Samiyeh Mahmoudian; Vladimir Dobrosavljević
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eye 5
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The Typical Medium Theory provides conceptually the simplest order parameter description of Anderson localization by self-consistently calculating the geometrically-averaged (typical) local density of states (LDOS). Here we show how spatial correlations can also be captured within such a self-consistent theory, by utilizing the standard Landau method of allowing for (slow) spatial fluctuations of the order parameter, and performing an appropriate gradient expansion. Our theoretical results...
Topics: Condensed Matter, Disordered Systems and Neural Networks
Source: http://arxiv.org/abs/1503.00420
2
2.0
Jun 30, 2018
06/18
by
Oded Agam; Igor L. Aleiner
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eye 2
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There are three basic processes that determine hopping transport: (a) hopping between normally empty sites (i.e. having exponentially small occupation numbers at equilibrium); (b) hopping between normally occupied sites, and (c) transitions between normally occupied and unoccupied sites. In conventional theories all these processes are considered Markovian and the correlations of occupation numbers of different sites are believed to be small(i.e. not exponential in temperature). We show that,...
Topics: Disordered Systems and Neural Networks, Condensed Matter
Source: http://arxiv.org/abs/1404.3981
3
3.0
Jun 30, 2018
06/18
by
Laszlo Ujfalusi; Imre Varga
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eye 3
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The phase diagram of the metal-insulator transition in a three dimensional quantum percolation problem is investigated numerically based on the multifractal analysis of the eigenstates. The large scale numerical simulation has been performed on systems with linear sizes up to $L=140$. The multifractal dimensions, exponents $D_q$ and $\alpha_q$, have been determined in the range of $0\leq q\leq 1$. Our results confirm that this problem belongs to the same universality class as the three...
Topics: Disordered Systems and Neural Networks, Condensed Matter
Source: http://arxiv.org/abs/1405.1985
3
3.0
Jun 28, 2018
06/18
by
Abdelaali Boudjemaa
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eye 3
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We sudy the impact of a weak random potential with a Gaussian correlation function on the thermodynamics of a two-dimensional (2D) dipolar bosonic gas. Analytical expressions for the quantum depletion, anomalous density, the ground state energy, the equation of state and the sound velocity are derived in the roton regime within the framework of the Bogoliubov theory. Surprisingly, we find that the condensate depletion and the anomalous density are comparable. The structure factor and the...
Topics: Disordered Systems and Neural Networks, Condensed Matter
Source: http://arxiv.org/abs/1509.08506
3
3.0
Jun 30, 2018
06/18
by
I. M. Suslov
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Using the well-known "algebra of multifractality", we derive the functional equation for anomalous dimensions \Delta_q, whose solution \Delta_q=aq(q-1) corresponds to strict parabolicity of the multifractal spectrum. This result demonstrates clearly that a correspondence of \sigma-models with the initial disordered systems is not exact.
Topics: Disordered Systems and Neural Networks, Condensed Matter
Source: http://arxiv.org/abs/1412.5339
2
2.0
Jun 28, 2018
06/18
by
Vassiliy Lubchenko
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The random first-order transition (RFOT) theory of the structural glass transition is reviewed in a pedagogical fashion. The rigidity that emerges in crystals and glassy liquids is of the same fundamental origin. In both cases, it corresponds with a breaking of the translational symmetry; analogies with freezing transitions in spin systems can also be made. The common aspect of these seemingly distinct phenomena is a spontaneous emergence of the molecular field, a venerable and well-understood...
Topics: Disordered Systems and Neural Networks, Condensed Matter
Source: http://arxiv.org/abs/1511.05998
2
2.0
Jun 29, 2018
06/18
by
K. S. Tikhonov; A. D. Mirlin
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eye 2
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We investigate analytically and numerically eigenfunction statistics in a disordered system on a finite Bethe lattice (Cayley tree). We show that the wave function amplitude at the root of a tree is distributed fractally in a large part of the delocalized phase. The fractal exponents are expressed in terms of the decay rate and the velocity in a problem of propagation of a front between unstable and stable phases. We demonstrate a crucial difference between a loopless Cayley tree and a locally...
Topics: Disordered Systems and Neural Networks, Condensed Matter
Source: http://arxiv.org/abs/1608.00331
2
2.0
Jun 30, 2018
06/18
by
J. A. Mendez-Bermudez; Guilherme Ferraz de Arruda; Francisco A. Rodrigues; Yamir Moreno
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eye 2
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We demonstrate that the normalised localization length $\beta$ of the eigenfunctions of diluted (sparse) banded random matrices follows the scaling law $\beta=x^*/(1+x^*)$. The scaling parameter of the model is defined as $x^*\propto(b_{eff}^2/N)^\delta$, where $b_{eff}$ is the average number of non-zero elements per matrix row, $N$ is the matrix size, and $\delta\sim 1$. Additionally, we show that $x^*$ also scales the spectral properties of the model (up to certain sparsity) characterized by...
Topics: Disordered Systems and Neural Networks, Condensed Matter
Source: http://arxiv.org/abs/1701.01484
2
2.0
Jun 30, 2018
06/18
by
Alexander L. Burin
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Many-body localization transition in a periodically driven quantum system is investigated using a solution of a matching Bethe lattice problem for Floquet states of a quantum random energy model with a generalization to more realistic settings. It turns out that an external periodic field can both suppress and enhance localization depending on field amplitude and frequency which leads to three distinguishable regimes of field enhanced, controlled and suppressed delocalization. The results can...
Topics: Disordered Systems and Neural Networks, Condensed Matter
Source: http://arxiv.org/abs/1702.01431
2
2.0
Jun 29, 2018
06/18
by
Hiroaki S. Yamada
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In the previous work, we investigated the correlation-induced localization-delocalization transition (LDT) of the wavefunction at band center ($E=0$) in the one-dimensional tight-binding model with fractal disorder [Yamada, EPJB (2015) 88, 264]. In the present work, we study the energy ($E \neq 0$) dependence of the normalized localization length and the delocalization of the wavefunction at the different energy in the same system. The mobility edges in the LDT arise when the fractal dimension...
Topics: Disordered Systems and Neural Networks, Condensed Matter
Source: http://arxiv.org/abs/1602.07926
2
2.0
Jun 29, 2018
06/18
by
Benedikt Krüger; Ella M. Schmidt; Klaus Mecke
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Random unimodular lattice triangulations have been recently used as an embedded random graph model, which exhibit a crossover behaviour between an ordered, large-world and a disordered, small-world behaviour. Using the ergodic Pachner flips that transform such triangulations into another and an energy functional that corresponds to the degree distribution variance, Markov chain Monte-Carlo simulations can be applied to study these graphs. Here, we consider the spectra of the adja cency and the...
Topics: Disordered Systems and Neural Networks, Condensed Matter
Source: http://arxiv.org/abs/1603.00265
2
2.0
Jun 29, 2018
06/18
by
Cecile Monthus
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eye 2
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For short-ranged disordered quantum models in one dimension, the Many-Body-Localization is analyzed via the adaptation to the Many-Body context [M. Serbyn, Z. Papic and D.A. Abanin, PRX 5, 041047 (2015)] of the Thouless point of view on the Anderson transition : the question is whether a local interaction between two long chains is able to reshuffle completely the eigenstates (Delocalized phase with a volume-law entanglement) or whether the hybridization between tensor states remains limited...
Topics: Disordered Systems and Neural Networks, Condensed Matter
Source: http://arxiv.org/abs/1603.04701
4
4.0
Jun 30, 2018
06/18
by
Indubala Satija
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eye 4
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We revisit the problem of self-similar properties of the Hofstadter butterfly spectrum, focusing on spectral as well as topological characteristics. In our studies involving any value of magnetic flux and arbitrary flux interval, we single out the most dominant hierarchy in the spectrum, which is found to be associated with an irrational number $\zeta=2+\sqrt{3}$ where nested set of butterflies describe a kaleidoscope. Characterizing an intrinsic frustration at smallest energy scale, this...
Topics: Disordered Systems and Neural Networks, Condensed Matter
Source: http://arxiv.org/abs/1408.1006
2
2.0
Jun 30, 2018
06/18
by
Ludovica Bachschmid Romano; Manfred Opper
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eye 2
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We consider the problem of predicting the spin states in a kinetic Ising model when spin trajectories are observed for only a finite fraction of sites. In a Bayesian setting, where the probabilistic model of the spin dynamics is assumed to be known, the optimal prediction can be computed from the conditional (posterior) distribution of unobserved spins given the observed ones. Using the replica method, we compute the error of the Bayes optimal predictor for parallel discrete time dynamics in a...
Topics: Disordered Systems and Neural Networks, Condensed Matter
Source: http://arxiv.org/abs/1405.4164
3
3.0
Jun 29, 2018
06/18
by
Thomas Wellens; Rodolfo A. Jalabert
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We develop a self-consistent theory describing the spin and spatial electron diffusion in the impurity band of doped semiconductors under the effect of a weak spin-orbit coupling. The resulting low-temperature spin-relaxation time and diffusion coefficient are calculated within different schemes of the self-consistent framework. The simplest of these schemes qualitatively reproduces previous phenomenological developments, while more elaborate calculations provide corrections that approach the...
Topics: Disordered Systems and Neural Networks, Condensed Matter
Source: http://arxiv.org/abs/1604.03917
3
3.0
Jun 29, 2018
06/18
by
Francesco Concetti
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In this paper, we study the thermodynamic properties of a system of $D$-components classical Heisenberg spins lying on the vertices of a random regular graph, with an unconventional first neighbor non-random interaction $J(\mathbf{S}_i\cdot \mathbf{S}_k)^2$. We can consider this model as a continuum version of anti-ferromagnetic $D$-states Potts model. We compute the paramagnetic free energy, using a new approach, presented in this paper for the first time, based on the replica method. Through...
Topics: Disordered Systems and Neural Networks, Condensed Matter
Source: http://arxiv.org/abs/1604.08190
2
2.0
Jun 29, 2018
06/18
by
Vedika Khemani; S. P. Lim; D. N. Sheng; David A. Huse
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The transition from a many-body localized phase to a thermalizing one is a dynamical quantum phase transition which lies outside the framework of equilibrium statistical mechanics. We provide a detailed study of the critical properties of this transition at finite sizes in one dimension. We find that the entanglement entropy of small subsystems looks strongly subthermal in the quantum critical regime, which indicates that it varies discontinuously across the transition as the system-size is...
Topics: Disordered Systems and Neural Networks, Condensed Matter
Source: http://arxiv.org/abs/1607.05756
5
5.0
Jun 29, 2018
06/18
by
Do-Hyun Kim; Jinha Park; B. Kahng
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eye 5
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The Hopfield model is a paradigmatic model for understanding neural activities associated with memory retrieval in view of the collective behavior of neurons. The analytical solution of the model on fully connected networks revealed that information stored in the memory can be retrieved without any error up to a certain threshold of storage capacity, beyond which the information is completely lost. A normal human brain, however, has imperfect memory with some error even when its storage...
Topics: Disordered Systems and Neural Networks, Condensed Matter
Source: http://arxiv.org/abs/1608.01071
2
2.0
Jun 29, 2018
06/18
by
Andrea Pagnani; Giorgio Parisi
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We study the Restricted Solid on Solid model for surface growth in spatial dimension $d=2$ by means of a multi-surface coding technique that allows to produce a large number of samples of samples in the stationary regime in a reasonable computational time. Thanks to: (i) a careful finite-size scaling analysis of the critical exponents, (ii) the accurate estimate of the first three moments of the height fluctuations, we can quantify the wandering exponent with unprecedented precision:...
Topics: Disordered Systems and Neural Networks, Condensed Matter
Source: http://arxiv.org/abs/1611.08445
9
9.0
Jun 28, 2018
06/18
by
V. E. Kravtsov; I. M. Khaymovich; E. Cuevas; M. Amini
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eye 9
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Motivated by the problem of Many-Body Localization and the recent numerical results for the level and eigenfunction statistics on the random regular graphs, a generalization of the Rosenzweig-Porter random matrix model is suggested that possesses two localization transitions as the parameter $\gamma$ of the model varies from 0 to $\infty$. One of them is the Anderson transition from the localized to the extended states that happens at $\gamma=2$. The other one at $\gamma=1$ is the transition...
Topics: Disordered Systems and Neural Networks, Condensed Matter
Source: http://arxiv.org/abs/1508.01714
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8.0
Jun 26, 2018
06/18
by
Santanu Sinha; Jonas T. Kjellstadli; Alex Hansen
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We consider the local load sharing fiber bundle model in one to five dimensions. Depending on the breaking threshold distribution of the fibers, there is a transition where the fracture process becomes localized. In the localized phase, the model behaves as the invasion percolation model. The difference between the local load sharing fiber bundle model and the equal load sharing fiber bundle model decreases with increasing dimensionality as a power law.
Topics: Condensed Matter, Disordered Systems and Neural Networks
Source: http://arxiv.org/abs/1501.02489
10
10.0
Jun 27, 2018
06/18
by
Alain Billoire
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We present results of a Monte Carlo study of the equilibrium dynamics of the one dimensional long-range Ising spin glass model. By tuning a parameter $\sigma$, this model interpolates between the mean field Sherrington-Kirkpatrick model and a proxy of the finite dimensional Edward-Anderson model. Activated scaling fits for the behavior of the relaxation time $\tau$ as a function of the number of spins $N$ (Namely $\ln(\tau)\propto N^{\psi}$) give values of $\psi$ that are not stable against...
Topics: Disordered Systems and Neural Networks, Condensed Matter
Source: http://arxiv.org/abs/1505.00676
14
14
Jun 28, 2018
06/18
by
Daniel Jung; Keith Slevin; Stefan Kettemann
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eye 14
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We study effects of classical magnetic impurities on the Anderson metal-insulator transition numerically. We find that a small concentration of Heisenberg impurities enhances the critical disorder amplitude $W_{\rm c}$ with increasing exchange coupling strength $J$. The resulting scaling with $J$ is analyzed which supports an anomalous scaling prediction by Wegner due to the combined breaking of time-reversal and spin-rotational symmetry. Moreover, we find that the presence of magnetic...
Topics: Disordered Systems and Neural Networks, Condensed Matter
Source: http://arxiv.org/abs/1507.03374
2
2.0
Jun 30, 2018
06/18
by
S. Bhardwaj; I. A. Gruzberg; V. Kagalovsky
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We study relevant perturbations at the spin quantum Hall critical point using a network model formulation. The model has been previously mapped to classical percolation on a square lattice, and we use the mapping to extract exact analytical values of the scaling dimensions of the relevant perturbations. We find that several perturbations that are distinct in the network model formulation correspond to the same operator in the percolation picture. We confirm our analytical results by comparing...
Topics: Disordered Systems and Neural Networks, Condensed Matter
Source: http://arxiv.org/abs/1412.1812
3
3.0
Jun 30, 2018
06/18
by
K. Ziegler
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Anderson localization is studied for two-dimensional Dirac fermions in the presence of strong random scattering. Averaging with respect to the latter leads to a graphical representation of the correlation function with entangled random walks and three-vertices which connect three different types of propagators. This approach indicates Anderson localization along a semi-infinite line, where the localization length is inversely proportional to the scattering rate.
Topics: Disordered Systems and Neural Networks, Condensed Matter
Source: http://arxiv.org/abs/1412.7732
10
10.0
Jun 27, 2018
06/18
by
Martin R. Zirnbauer
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eye 10
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Quantum mechanical systems with some degree of complexity due to multiple scattering behave as if their Hamiltonians were random matrices. Such behavior, while originally surmised for the interacting many-body system of highly excited atomic nuclei, was later discovered in a variety of situations including single-particle systems with disorder or chaos. A fascinating theme in this context is the emergence of universal laws for the fluctuations of energy spectra and transport observables. After...
Topics: Condensed Matter, Disordered Systems and Neural Networks
Source: http://arxiv.org/abs/1503.08964
5
5.0
Jun 30, 2018
06/18
by
Anthony C. Vasko; Aarohi Vijh; Victor G. Karpov
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We present data exhibiting hot spots spontaneously emerging in forward biased thin film photovoltaics based on a-Si:H technology. These spots evolve over time shrinking in their diameter and increasing temperature up to approximately 300 $^o$C above that of the surrounding area. Our numerical approach explores a system of many identical diodes in parallel connected through the resistive electrode and through thermal connectors, a model which couples electric and thermal processes. The modeling...
Topics: Disordered Systems and Neural Networks, Condensed Matter
Source: http://arxiv.org/abs/1401.0056
2
2.0
Jun 30, 2018
06/18
by
G. G. Kozlov
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Tight-binding 1D random system with long-range correlations is studied numerically using the localisation criterium, which represents the number of sites, covered by the wave function. At low degrees of disorder the signs of a mobility edge, predicted in \cite{Izr}, were found. The possibility of exact mobility edge in the system under consideration is discussed.
Topics: Disordered Systems and Neural Networks, Condensed Matter
Source: http://arxiv.org/abs/1403.0394
3
3.0
Jun 30, 2018
06/18
by
Alejandro Gaita-Ariño; Vicente F. González-Albuixech; Moshe Schechter
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The bias energies of various two-level systems (TLSs) and their strengths of interactions with the strain are calculated for Ar:N$_2$ glass. Unlike the case in KBr:CN, a distinct class of TLSs having weak interaction with the strain and untypically small bias energies is not found. The addition of CO molecules introduces CO flips which form such a class of weakly interacting TLSs, albeit at much lower coupling than are typically observed in solids. We conclude that because of the absence of a...
Topics: Disordered Systems and Neural Networks, Condensed Matter
Source: http://arxiv.org/abs/1405.2217
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4.0
Jun 30, 2018
06/18
by
Takeshi Egami; Koshiro Suzuki; Katsuhiro Watanabe
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A novel Einstein relation (fractional Einstein relation, FER) for the electric conduction in non-crystalline semiconductors is presented. FER and the generalized Einstein relation (GER) [Phys. Rev. E 8, 1296 (1998)] are compared to the result of the Monte Carlo (MC) simulation, and is confirmed that FER exhibits better agreement than GER. The cruial feature of FER is that it reflects the violation of the detailed balance in the coarse-grained hopping process, while it is preserved in the...
Topics: Disordered Systems and Neural Networks, Condensed Matter
Source: http://arxiv.org/abs/1406.0226
2
2.0
Jun 30, 2018
06/18
by
P. H. Lundow; I. A. Campbell
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The critical behavior of the Binder cumulant for Ising spin glasses in dimension four are studied through simulation measurements. Data for the bimodal interaction model are compared with those for the Laplacian interaction model. Special attention is paid to scaling corrections. The limiting infinite size value at criticality for this dimensionless variable is a parameter characteristic of a universality class. This critical limit is estimated to be equal to $0.523(3)$ in the bimodal model and...
Topics: Disordered Systems and Neural Networks, Condensed Matter
Source: http://arxiv.org/abs/1411.2155
2
2.0
Jun 30, 2018
06/18
by
Jun-ichi Inoue
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We present a brief review on information processing, computing and inference via quantum fluctuation, and clarify the relationship between the probabilistic information processing and theory of quantum spin glasses through the analysis of the infinite-range model. We also argue several issues to be solved for the future direction in the research field.
Topics: Disordered Systems and Neural Networks, Condensed Matter
Source: http://arxiv.org/abs/1409.4871
2
2.0
Jun 29, 2018
06/18
by
Isaac Weinberg; Yaron de Leeuw; Tsampikos Kottos; Doron Cohen
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We consider thermal transport in low-dimensional disordered harmonic networks of coupled masses. Utilizing known results regarding Anderson localization, we derive the actual dependence of the thermal conductance $G$ on the length $L$ of the sample. This is required by nanotechnology implementations because for such networks Fourier's law $G \propto 1/L^{\alpha}$ with $\alpha=1$ is violated. In particular we consider "glassy" disorder in the coupling constants, and find an anomaly...
Topics: Disordered Systems and Neural Networks, Condensed Matter
Source: http://arxiv.org/abs/1601.02207
2
2.0
Jun 29, 2018
06/18
by
Felix Thiel; Igor M. Sokolov
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We consider the random walk on a lattice with random transition rates and arbitrarily long-range jumps. We employ Bruggeman's effective medium approximation (EMA) to find the disorder averaged (coarse-grained) dynamics. The EMA procedure replaces the disordered system with a cleverly guessed reference system in a self-consistent manner. We give necessary conditions on the reference system and discuss possible physical mechanisms of anomalous diffusion. In case of a power-law scaling between...
Topics: Disordered Systems and Neural Networks, Condensed Matter
Source: http://arxiv.org/abs/1604.06621
