Year: 2016
Type: article
Abstract: Randomly coupled Ising spins constitute the classical model of collective phenomena in disordered systems, with applications covering glassy magnetism and frustration, combinatorial optimization, protein folding, stock market dynamics, and social dynamics.The phase diagram of these systems is obtained in the thermodynamic limit by averaging over the quenched randomness of the couplings.However, many applications require the statistics of activity for a single realization of the possibly asymmetric couplings in finite-sized networks.Examples include reconstruction of couplings from the observed dynamics, representation of probability distributions for sampling-based inference, and learning in the central nervous system based on the dynamic and correlation-dependent modification of synaptic connections.The systematic cumulant expansion for kinetic binary (Ising) threshold units with strong, random, and asymmetric couplings presented here goes beyond mean-field theory and is applicable outside thermodynamic equilibrium; a system of approximate nonlinear equations predicts average activities and pairwise covariances in quantitative agreement with full simulations down to hundreds of units.The linearized theory yields an expansion of the correlation and response functions in collective eigenmodes, leads to an efficient algorithm solving the inverse problem, and shows that correlations are invariant under scaling of the interaction strengths.
Source: Physical Review X
Authors: David Dahmen, Hannah Bos, Moritz Helias
Language: English
Subfield: Condensed Matter Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $4,200
Funder: Seventh Framework Programme
Award: G8750896698
OpenAlex ID: W2257845457