  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.
