Description of Some Ground States by Puiseux Techniques

摘要

Let (σ_+~G)be a one-sided transitive subshift of finite type, where symbols are given by a finite spin set S, and admissible transitions are represented by an irreducible directed graph G?S×S. Let H:σ~+_Gbe a locally constant function (that corresponds with a local observable which makes finite-range interactions).Given β>0, let μ_(βH) be the Gibbs-equilibrium probability measure associated with the observable -βH. It is known, by using abstract considerations, that {μ_(βH)}_(β>0) converges as β→+∞ to a H-minimizing probability measure μ~H_(min) called zero-temperature Gibbs measure. For weighted graphs with a small number of vertices, we describe here an algorithm (similar to the Puiseux algorithm) that gives the explicit form of μ~H_(min) on the set of ground-state configurations.