Exact statistical mechanics of the Ising model on networks

TL;DR

This paper presents an exact method to compute the Ising model's partition function on networks with small tree-width, applicable to many real and model networks, advancing understanding of finite-size disordered systems.

Contribution

It introduces a novel exact approach leveraging small tree-width to evaluate the Ising partition function on complex networks.

Findings

Exact evaluation of the Ising partition function on networks with small tree-width

Applicable to both empirical and model-generated networks

Advances the analysis of finite disordered systems

Abstract

The Ising model is an equilibrium stochastic process used as a model in several branches of science including magnetic materials, geophysics, neuroscience, sociology and finance. Real systems of interest have finite size and a fixed coupling matrix exhibiting quenched disorder. Exact methods for the Ising model, however, employ infinite size limits, translational symmetries of lattices and the Cayley tree, or annealed structures as ensembles of networks. Here we show how the Ising partition function can be evaluated exactly by exploiting small tree-width. This structural property is exhibited by a large set of networks, both empirical and model generated.