Generalization of the Peierls-Griffiths Theorem for the Ising Model on Graphs

TL;DR

This paper establishes a sufficient condition related to graph topology that guarantees spontaneous magnetization in the Ising model, demonstrating phase transitions on various networks.

Contribution

It generalizes the Peierls-Griffiths theorem to arbitrary graphs, linking topology to phase transition phenomena in the Ising model.

Findings

Proves phase transition existence at T > 0 on broad network classes

Introduces a topological condition for spontaneous magnetization

Extends classical results to complex graph structures

Abstract

We present a sufficient condition for the presence of spontaneous magnetization for the Ising model on a general graph, related to its long-range topology. Applying this condition we are able to prove the existence of a phase transition at temperature T > 0 on a wide class of general networks. The possibility of further extensions of our results is discussed.