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Exact statistical mechanics of the Ising model on networks

2021/11/08 by Konstantin Klemm, Klemm, Konstantin
Physics and Astronomy · #Complex Network Analysis Techniques #Disordered Systems and Neural Networks (cond-mat.dis-nn) #FOS: Physical sciences #Opinion Dynamics and Social Influence #Statistical Mechanics (cond-mat.stat-mech) #Theoretical and Computational Physics

paper · pdf · doi:10.48550/arxiv.2111.04766

openalex publication_date 2021/11/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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