Marked Gibbs measures via cluster expansion

Details Marked Gibbs measures via cluster expansion Marked Gibbs measures via cluster expansion

1999-08-04

arxiv.org/abs/math-ph/9908006v1

Methods of Functional Analysis and topology 4(4) 51-81, 1998

Physics

Mathematical Physics

51 pages

Scientific paper

We give a sufficiently detailed account on the construction of marked Gibbs measures in the high temperature and low fugacity regime. This is proved for a wide class of underlying spaces and potentials such that stability and integrability conditions are satisfied. That is, for state space we take a locally compact separable metric space $X$ and a separable metric space $S$ for the mark space. This framework allowed us to cover several models of classical and quantum statistical physics. Furthermore, we also show how to extend the construction for more general spaces as e.g., separable standard Borel spaces. The construction of the marked Gibbs measures is based on the method of cluster expansion.

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