Large deviations for the $\nabla\varphi$ interface model with self potentials

Abstract

The aim of this paper is to study, in the framework of the $\nabla\varphi$ interface model, the macroscopic behavior of microscopic interfaces under the finite volume Gibbs measures with self potentials, especially by establishing the large deviation principle. We consider the case where the self potential depends on the position and on both macroscopic and microscopic heights of the interfaces as well. The assumption on the upper bound for the self potential required by [10] is relaxed.