A Phase Transition in a Quantum Crystal with Asymmetric Potentials

Details A Phase Transition in a Quantum Crystal with Asymmetric Potentials A Phase Transition in a Quantum Crystal with Asymmetric Potentials

2006-11-08

arxiv.org/abs/math-ph/0611017v1

Physics

Mathematical Physics

15 pages

Scientific paper

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.

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