Marked Gibbs measures via cluster expansion

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...

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Bibliographic Details
Published in:arXiv.org 1999-08
Main Authors: Kondratiev, Yuri, Kuna, Tobias, Silva, Jose Luis
Format: Article
Language:English
Subjects:
Clusters
Fugacity
High temperature
Integral calculus
Metric space
Quantum statistics
Online Access:Get full text
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Summary: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.
ISSN:2331-8422