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Uniqueness of a Gibbs field with random potential. An elementary approach. (English. Russian original) Zbl 0635.60107
Theory Probab. Appl. 31, 572-589 (1987); translation from Teor. Veroyatn. Primen. 31, No. 4, 651-670 (1986).
This paper provides a new proof for the uniqueness result of Gibbs states for random interaction potentials on a regulr lattice of arbitrary dimension in the high temperature regime [see e.g. J. Fröhlich and J. Imbrie, Commun. Math. Phys. 96, 145-180 (1984; Zbl 0574.60098)]. Instead of the cluster expansion method, the authors proceed by associating to each realization of the random interaction potential a new random graph. They show then via an induction procedure where certain vertices of the graph are “unglued”, that these graphs bear almost surely a unique Gibbs field, if the interaction force is small.
Reviewer: Th.Eisele

MSC:
60K35 Interacting random processes; statistical mechanics type models; percolation theory
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