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For a class of $\zz^2$ Markov Random Fields (MRFs) $\mu$, we show that thesequence of successive differences of entropies of induced MRFs on strips ofheight $n$ converges exponentially fast (in $n$) to the entropy of $\mu$. Thesestrip entropies can be computed explicitly when $\mu$ is a Gibbs state given bya nearest-neighbor interaction on a strongly irreducible nearest-neighbor$\zz^2$ shift of finite type $X$. We state this result in terms ofapproximations to the (topological) pressures of certain functions on such an$X$, and we show that these pressures are computable if the values taken on bythe functions are computable. Finally, we show that our results apply to thehard core model and Ising model for certain parameter values of thecorresponding interactions, as well as to the topological entropy of certainnearest-neighbor $\zz^2$ shifts of finite type, generalizing a result in\cite{Pa}.

Approximating entropy for a class of $\zz^2$ Markov Random Fields and pressure for a class of functions on $\zz^2$ shifts of finite type