Uniqueness of Gibbs states for general \(P(\phi)_ 2\)-weak coupling models by cluster expansion
Quantum fields with weak coupling in two space-time dimensions are considered. The basic theorem of this paper states that for general \(P(\phi)_ 2\)-weak coupling models with sufficiently small coupling constant the set of all ultra regular Gibbs states consists only of one point which is an extremal Gibbs state. In the proof are used the method of cluster expansion in the sense of Glimm, Jaffé and Spencer, as well as the estimates of the solutions of the Dirichlet problem with distributional data and the representation of ultra regular measures in the sense of \textit{J. Fröhlich} and \textit{B. Simon} [see Ann. Math. 105, 493-526 (1977)].
scientific article; zbMATH DE number 4145102
scientific article