Title: QUANTUM ANHARMONIC CRYSTAL IN FUNCTIONAL INTEGRAL APPROACH
Author(s): Yu.Kondratiev (Fakult{\"a}t f{\"u}r Mathematik, Universit{\"a}t Bielefeld, D 33615 Bielefeld, Germany; Forschungszentrum BiBoS, Bielefeld, Germany; Institute of Mathematics, Kiev, Ukraine) , Yu.Kozitsky (Instytut Matematyki, Uniwersytet Marii Curie-Sk{\l}odowskiej w Lublinie, PL 20-031 Lublin, Poland) , T.Pasurek (Fakult{\"a}t f{\"u}r Mathematik, Universit{\"a}t Bielefeld, D 33615 Bielefeld, Germany; Forschungszentrum BiBoS, Bielefeld, Germany) , M.R{\"o}ckner (Fakult{\"a}t f{\"u}r Mathematik, Universit{\"a}t Bielefeld, D 33615 Bielefeld, Germany; Forschungszentrum BiBoS, Bielefeld, Germany)

A lattice model of interacting light quantum particles of mass $m$ oscillating in a crystalline field is considered in the framework of an approach based on functional integrals. The main aspects of this approach are described on an introductory level. Then a mechanism of the stabilization of this model by quantum effects is suggested. In particular, a stability condition involving $m$, the interaction intensity, and the parameters of the crystalline field is given. It is independent of the temperature and is satisfied if $m$ is small enough and/or the tunnelling frequency is big enough. It is shown that under this condition the infinite-volume correlation function decays exponentially; hence, no phase transitions can arise at all temperatures.

Key words: quantum stabilization, Gibbs states, soft mode
PACS: 05.50.-d, 64.60.-i