Decay of covariances, uniqueness of ergodic component and scaling limit for a class of \nabla\phi systems with non-convex potential

TL;DR

This paper investigates a lattice gradient interface model with non-convex potentials, establishing key properties like ergodic measure uniqueness, covariance decay, scaling limits, and surface tension convexity.

Contribution

It introduces a decoupling technique for non-convex potentials, proving fundamental properties of the abla ext{ extphi}-Gibbs measures in this setting.

Findings

Proves uniqueness of ergodic components for the model

Demonstrates decay of covariances in the system

Establishes the scaling limit and convexity of surface tension

Abstract

We consider a gradient interface model on the lattice with interaction potential which is a nonconvex perturbation of a convex potential. Using a technique which decouples the neighboring vertices sites into even and odd vertices, we show for a class of non-convex potentials: the uniqueness of ergodic component for \nabla\phi-Gibbs measures, the decay of covariances, the scaling limit and the strict convexity of the surface tension.