  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.
