New techniques for pressure approximation in Z^d shift spaces

Given a Z^d shift of finite type and a nearest-neighbour interaction, we present sufficient conditions for efficient approximation of pressure and, in particular, topological entropy. Among these conditions, we introduce a combinatorial analog of the measure-theoretic property of Gibbs measures known as strong spatial mixing and we show that it implies many desirable properties in the context of symbolic dynamics. Next, we apply our results to some classical 2-dimensional statistical mechanics models such as the (ferromagnetic) Potts, (multi-type) Widom-Rowlinson, and hard-core lattice gas models for certain subsets of both the subcritical and supercritical regimes. The approximation techniques make use of a special representation theorem for pressure that may be of independent interest.

Part of this talk is joint work with Stefan Adams, Brian Marcus, and Ronnie Pavlov.