In the context of stationary Zd nearest-neighbour Gibbs measures
μ satisfying strong spatial mixing, we present a new combinatorial
condition (the topological strong spatial mixing property (TSSM)) on the
support of μ sufficient for having an efficient approximation algorithm for
topological pressure. We establish many useful properties of TSSM for studying
strong spatial mixing on systems with hard constraints. We also show that TSSM
is, in fact, necessary for strong spatial mixing to hold at high rate. Part of
this work is an extension of results obtained by D. Gamarnik and D. Katz
(2009), and B. Marcus and R. Pavlov (2013), who gave a special representation
of topological pressure in terms of conditional probabilities.Comment: 40 pages, 8 figures. arXiv admin note: text overlap with
arXiv:1309.1873 by other author