Thermal fluctuations around classical crystalline ground states. The case of bounded fluctuations

TL;DR

This paper investigates low-temperature thermal fluctuations in classical crystalline systems, deriving a cluster expansion for bounded fluctuations and establishing nonperturbative results on Gibbs states for dipole interactions.

Contribution

It introduces a low-temperature cluster expansion for bounded thermal fluctuations and proves existence and boundary condition independence of Gibbs states in dipole systems.

Findings

Derived a cluster expansion for free energy contributions.

Proved existence of Gibbs states independent of boundary conditions.

Analyzed behavior of long-range interacting dipole systems at high temperature and density.

Abstract

We study low--temperature non Gaussian thermal fluctuations of a system of classical particles around a (hypothetical) crystalline ground state. These thermal fluctuations are described by the behaviour of a system of long range interacting charged dipoles at high--temperature and high--density. For the case of uniformly bounded fluctuations, the low--temperature linked cluster expansion describing the contribution to the free energy is derived and analysed. Finally some nonpertubative results on the existence and independence of boundary conditions of the Gibbs states for the associated dipole systems are obtained.