The critical Ising model on amenable graphs of exponential growth

Abstract

The purpose of this note is to point out that the proof of the recent result of Hutchcroft [Hut] concerning continuity of the phase transition in Bernoulli percolation is applicable to the setting of the Ising model with free boundary conditions. This observation, together with a recent result of Aizenman, Duminil-Copin, and Sidoravicius [ADS] implies that the Ising model on any amenable transitive graph with exponential growth undergoes a continuous phase transition.