Alina Kargol and Yuri Kozitsky
A Phase Transition in a Quantum 
Crystal with Asymmetric Potentials
(323K, pdf)

ABSTRACT.  A translation invariant system of interacting quantum anharmonic 
oscillators indexed by the elements of a simple cubic lattice 
$\mathbb{Z}^d$ is considered. The anharmonic potential is of general 
type, which in particular means that it might have no symmetry. For 
this system, we prove that the global polarization (obtained in the 
thermodynamic limit) gets discontinuous at a certain value of the 
external field provided $d\geq 3$, and the particle mass as well as 
the interaction intensity are big enough. The proof is based on the 
representation of local Gibbs states in terms of path measures and 
thereby on the use of the infrared estimates and the 
Garsia-Rodemich-Rumsey inequality.