PUB - Publikationen an der Universität Bielefeld

A model of interacting quantum particles performing one-dimensional anharmonic oscillations around their unstable equilibrium positions, which form the lattice Z(d) is considered. For this model, two statements describing its equilibrium properties are given. The first theorem states that there exists m(*) > 0 such that for all values of the particle mass m < m(*), the set of tempered Euclidean Gibbs measures consists of exactly one element at all values of the temperature β(-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 [1] where the boundary m(*) depended on β in such a way that m(*)(β) --> 0 for beta --> +infinity. The second theorem states that the two-point correlation function has an exponential decay if m < m(*).