Small mass implies uniqueness of Gibbs states of a quantum crystal
A model of interacting quantum particles performing one-dimensional anharmonic oscillations around their equilibrium positions which form a lattice Z(d) is considered. For this model, it is proved that the set of tempered Euclidean Gibbs measures is a singleton provided the particle mass is less than a certain bound m(*), which is independent of the temperature beta(-1). This settles a problem that was open for a long time and is an essential improvement of a similar result proved before by the same authors [5], where the bound m(*) depended on beta in such a way that m(*) (beta) --> 0 as beta --> +infinity.
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69-90
SPRINGER-VERLAG