25,921 research outputs found
Spin glass polynomial identities from entropic constraints
No full textThe core idea of stochastic stability is that thermodynamic observables must be robust under small (random) perturbations of the quenched Gibbs measure. Combining this idea with the cavity field technique, which aims to measure the free energy increment under addition of a spin to the system, we sketch how to write a stochastic stability approach to diluted mean field spin glasses which explicitly gives overlap constraints as the outcome. We then show that, under minimal mathematical assumptions and for gauge-invariant systems (namely those with even Ising interactions), it is possible to 'reverse' the idea of stochastic stability and use it to derive a broad class of constraints on the unperturbed quenched Gibbs measure. This paper extends a previous study where we showed how to derive (linear) polynomial identities from the 'energy' contribution to the free energy, while here we focus on the consequences of 'entropic' constraints. Interestingly, in diluted spin glasses, the entropic approach generates more identities than those found by the energy route or other techniques. The two sets of identities become identical on a fully connected topology, where they reduce to the ones derived by Aizenman and Contucci
Market fragmentation and market consolidation: Multiple steady states in systems of adaptive traders choosing where to trade
Full text linkTechnological progress is leading to proliferation and diversification of trading venues, thus increasing the relevance of the long-standing question of market fragmentation versus consolidation. To address this issue quantitatively, we analyse systems of adaptive traders that choose where to trade based on their previous experience. We demonstrate that only based on aggregate parameters about trading venues, such as the demand to supply ratio, we can assess whether a population of traders will prefer fragmentation or specialization towards a single venue. We investigate what conditions lead to market fragmentation for populations with a long memory and analyse the stability and other properties of both fragmented and consolidated steady states. Finally we investigate the dynamics of populations with finite memory; when this memory is long the true long-time steady states are consolidated but fragmented states are strongly metastable, dominating the behaviour out to long times.<br/
Shear Induced Orientational Ordering in Active Glass
Full text linkDense assemblies of self propelled particles, also known as active or living
glasses are abundantaround us, covering different length and time scales: from
the cytoplasm to tissues, from bacterialbio-films to vehicular traffic jams,
from Janus colloids to animal herds. Being structurally disorderedas well as
strongly out of equilibrium, these systems show fascinating dynamical and
mechanicalproperties. Using extensive molecular dynamics simulation and a
number of different dynamicaland mechanical order parameters we differentiate
three dynamical steady states in a sheared modelactive glassy system: (a) a
disordered phase, (b) a propulsion-induced ordered phase, and (c)
ashear-induced ordered phase. We supplement these observations with an
analytical theory based onan effective single particle Fokker-Planck
description to rationalise the existence of the novel shear-induced
orientational ordering behaviour in our model active glassy system that has no
explicitaligning interactions,e.g.of Vicsek-type. This ordering phenomenon
occurs in the large persistencetime limit and is made possible only by the
applied steady shear. Using a Fokker-Planck descriptionwe make testable
predictions without any fit parameters for the joint distribution of single
particleposition and orientation. These predictions match well with the joint
distribution measured fromdirect numerical simulation. Our results are of
relevance for experiments exploring the rheologicalresponse of dense active
colloids and jammed active granular matter systems.Comment: 8 pages, 5 figure
Localization properties of the sparse Barrat-M\'ezard trap model
No full textInspired by works on the Anderson model on sparse graphs, we devise a method
to analyze the localization properties of sparse systems that may be solved
using cavity theory. We apply this method to study the properties of the
eigenvectors of the master operator of the sparse Barrat-M\'ezard trap model,
with an emphasis on the extended phase. As probes for localization, we consider
the inverse participation ratio and the correlation volume, both dependent on
the distribution of the diagonal elements of the resolvent. Our results reveal
a rich and non-trivial behavior of the estimators across the spectrum of
relaxation rates and an interplay between entropic and activation mechanisms of
relaxation that give rise to localized modes embedded in the bulk of extended
states. We characterize this route to localization and find it to be distinct
from the paradigmatic Anderson model or standard random matrix systems.Comment: 16 pages, 14 figures. Accepted in Physical Review
Multifractality and statistical localization in highly heterogeneous random networks
Full text linkWe consider highly heterogeneous random networks with symmetric interactions
in the limit of high connectivity. A key feature of this system is that the
spectral density of the corresponding ensemble exhibits a divergence within the
bulk. We study the structure of the eigenvectors associated with this
divergence and find that they are multifractal with the statistics of
eigenvector elements matching those of the resolvent entries. The corresponding
localization mechanism relies on the statistical properties of the nodes rather
than on any spatial structure around a localization centre. This "statistical
localization" mechanism is potentially relevant for explaining localization in
different models that display singularities in the bulk of the spectrum of
eigenvaluesComment: Accepted for publication in Europhysics Letters (EPL
Accurate dynamics from self-consistent memory in stochastic chemical reactions with small copy numbers
No full textAbstract We present a method that captures the fluctuations beyond mean field in chemical reactions in the regime of small copy numbers and hence large fluctuations, using self-consistently determined memory : by integrating information from the past we can systematically improve our approximation for the dynamics of chemical reactions. This memory emerges from a perturbative treatment of the effective action of the Doi-Peliti field theory for chemical reactions. By dressing only the response functions and by the self-consistent replacement of bare responses by the dressed ones, we show how a very small class of diagrams contributes to this expansion, with clear physical interpretations. From these diagrams, a large sub-class can be further resummed to infinite order, resulting in a method that is stable even for large values of the expansion parameter or equivalently large reaction rates. We demonstrate this method and its accuracy on single and multi-species binary reactions across a range of reaction constant values.International Max Planck Research School for the Physics of Biological and Complex System
Notes on the Polynomial Identities in Random Overlap Structures
No full textIn these notes we review first in some detail the concept of random overlap structure (ROSt) applied to fully connected and diluted spin glasses. We then sketch how to write down the general term of the expansion of the energy part from the Boltzmann ROSt (for the Sherrington-Kirkpatrick model) and the corresponding term from the RaMOSt, which is the diluted extension suitable for the Viana-Bray model. From the ROSt energy term, a set of polynomial identities (often known as Aizenman-Contucci or AC relations) is shown to hold rigorously at every order because of a recursive structure of these polynomials that we prove. We show also, however, that this set is smaller than the full set of AC identities that is already known. Furthermore, when investigating the RaMOSt energy for the diluted counterpart, at higher orders, combinations of such AC identities appear, ultimately suggesting a crucial role for the entropy in generating these constraints in spin glasses
Robust prediction of force chains in jammed solids using graph neural networks
No full textForce chains are quasi-linear self-organised structures carrying large stresses and are ubiquitous in jammed amorphous materials like granular materials, foams or even cell assemblies. Predicting where they will form upon deformation is crucial to describe the properties of such materials, but remains an open question. Here we demonstrate that graph neural networks (GNN) can accurately predict the location of force chains in both frictionless and frictional materials from the undeformed structure, without any additional information. The GNN prediction accuracy also proves to be robust to changes in packing fraction, mixture composition, amount of deformation, friction coefficient, system size, and the form of the interaction potential. By analysing the structure of the force chains, we identify the key features that affect prediction accuracy. Our results and methodology will be of interest for granular matter and disordered systems, e.g. in cases where direct force chain visualisation or force measurements are impossible
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