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

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.