The Burton-Steif correspondence: Statistical mechanics at the service of symbolic dynamics

Luis Armando Corona, Raul Salgado-Garcia, Edgardo Ugalde

Published 2021-04-15Version 1

Robert Burton and Jeffrey 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. In this paper, we study this correspondence, which in the cases we consider gives place to an isomorphism between a simplex of measures of maximal entropy of a strongly irreducible subshift of finite type and a simplex of equilibrium states of the corresponding statistical mechanics model. We illustrate this correspondence by using the Potts model and a model of our own, inspired by the vertex models in statistical mechanics.