A note on continuity of magnetization at criticality for the ferromagnetic Ising model on amenable quasi-transitive graphs with exponential growth

TL;DR

This paper extends recent percolation phase transition results to the Ising model on certain graphs, showing it undergoes a second order phase transition at criticality.

Contribution

It demonstrates that the proof techniques for Bernoulli percolation phase transitions are applicable to the Ising model on amenable quasi-transitive graphs with exponential growth.

Findings

Ising model exhibits second order phase transition on specified graphs.

Proof methods from percolation theory are applicable to the Ising model.

Phase transition continuity is established for the model.

Abstract

The purpose of this modest note is to point out that the proof of the recent result of Huchcroft concerning continuity of phase transition in Bernoulli percolation is applicable to the setting of the Ising model with free boundary condition. This observation, together with a recent result of Aizenman, Duminil-Copin, and Sidoravicius implies that the Ising model on amenable quasi-transitive graph with exponential growth undergoes a second order phase transition.