Uniqueness of Gibbs states of a quantum system on graphs

Details Uniqueness of Gibbs states of a quantum system on graphs Uniqueness of Gibbs states of a quantum system on graphs

2006-09-16

arxiv.org/abs/math-ph/0609046v1

Physics

Mathematical Physics

9 pages

Scientific paper

10.1016/S0034-4877(07)80064-4

Gibbs states of an infinite system of interacting quantum particles are considered. Each particle moves on a compact Riemannian manifold and is attached to a vertex of a graph (one particle per vertex). Two kinds of graphs are studied: (a) a general graph with locally finite degree; (b) a graph with globally bounded degree. In case (a), the uniqueness of Gibbs states is shown under the condition that the interaction potentials are uniformly bounded by a sufficiently small constant. In case (b), the interaction potentials are random. In this case, under a certain condition imposed on the probability distribution of these potentials the almost sure uniqueness of Gibbs states has been shown.

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