On the correspondence between Subshifts of Finite Type and Statistical Mechanics Models

TL;DR

This paper revisits and simplifies the correspondence between statistical mechanics models and symbolic dynamics, illustrating its applications to models like Potts and six-vertex, and exploring measures of maximal entropy.

Contribution

It provides a simplified exposition of the statistical mechanics and symbolic dynamics correspondence and demonstrates its applications to specific models.

Findings

Simplified the understanding of the correspondence between statistical mechanics and symbolic dynamics.

Applied the correspondence to analyze measures of maximal entropy in specific models.

Showcased the potential of this approach for studying complex systems.

Abstract

R. Burton and J. Steif developed a strategy to construct examples of strongly irreducible subshifts of finite type admitting several measures of maximal entropy. This strategy exploits a correspondence between equilibrium statistical mechanics and symbolic dynamics, correspondence which was later formalized by O. H\"aggstr\"om. In this paper, we revisit and discuss this correspondence with the aim of presenting a simplified version of it, and to expose some applications of rigorous results concerning the Potts model and the six-vertex model to symbolic dynamics, illustrating in this way of the possibilities of this correspondence.