Exact statistical mechanics of the Ising model on networks

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.

arXiv comment4 pages, 3 figures

References in corpus (13)

• Modularity and community structure in networks
• Finding community structure in networks using the eigenvectors of matrices
• Cooperative Game Theory Approaches for Network Partitioning
• Critical phenomena in complex networks
• Weak pairwise correlations imply strongly correlated network states in a neural population
• Pseudofractal Scale-free Web
• Highly clustered scale-free networks
• Ising Model on Networks with an Arbitrary Distribution of Connections
• Generic scale of the "scale-free" growing networks
• Ising models on locally tree-like graphs
• Message passing on networks with loops
• Predicting percolation thresholds in networks
• Beyond the locally tree-like approximation for percolation on real networks