Continuity of the Ising Phase Transition on Nonamenable Groups
Abstract
We prove rigorously that the ferromagnetic Ising model on any nonamenable Cayley graph undergoes a continuous (secondorder) phase transition in the sense that there is a unique Gibbs measure at the critical temperature. The proof of this theorem is quantitative and also yields powerlaw bounds on the magnetization at and near criticality. Indeed, we prove more generally that the magnetization ⟨σo⟩β,h+ is a locally Höldercontinuous function of the inverse temperature β and external field h throughout the nonnegative quadrant (β,h)∈[0,∞)2. As a second application of the methods we develop, we also prove that the free energy of Bernoulli percolation is twice differentiable at pc on any transitive nonamenable graph.
 Publication:

Communications in Mathematical Physics
 Pub Date:
 November 2023
 DOI:
 10.1007/s0022002304838y
 arXiv:
 arXiv:2007.15625
 Bibcode:
 2023CMaPh.404..227H
 Keywords:

 Mathematics  Probability;
 Mathematical Physics