Mixing length scales of low temperature spin plaquettes models

TL;DR

This paper rigorously analyzes the thermodynamic properties and correlation lengths of two-dimensional low temperature plaquette models, revealing unique Gibbs measures and self-similarity properties.

Contribution

It provides a rigorous study of the thermodynamics and correlation length scaling in 2D plaquette models, including exact self-similarity results.

Findings

Unique infinite volume Gibbs measure at positive temperature

Exponential decay of correlations

Exact self-similarity property of the Gibbs measure

Abstract

Plaquette models are short range ferromagnetic spin models that play a key role in the dynamic facilitation approach to the liquid glass transition. In this paper we perform a rigorous study of the thermodynamic properties of two dimensional plaquette models, the square and triangular plaquette models. We prove that for any positive temperature both models have a unique infinite volume Gibbs measure with exponentially decaying correlations. We analyse the scaling of three a priori different static correlation lengths in the small temperature regime, the mixing, cavity and multispin correlation lengths. Finally, using the symmetries of the model we determine an exact self similarity property for the infinite volume Gibbs measure.