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

Cotar, Codina; Deuschel, Jean-Dominique

Annales de l'I.H.P. Probabilités et statistiques, Tome 48 (2012) no. 3, pp. 819-853.

Nous considérons un modèle d'interfaces de type gradient indexé par le réseau avec une interaction donnée par la pertubation non convexe d'un potentiel convexe. En utilisant une technique qui découple les sites pairs et impairs, nous démontrons pour une classe de potentiels non convexes l'unicité de la composante ergodique, de la mesure de Gibbs du gradient, la décroissance des covariances, la loi limite centrale et la stricte convexité de la tension superficielle.

We consider a gradient interface model on the lattice with interaction potential which is a non-convex perturbation of a convex potential. Using a technique which decouples the neighboring vertices 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.

Classification : 60K35, 82B24, 35J15
Mots clés : effective non-convex gradient interface models, uniqueness of ergodic component, decay of covariances, scaling limit, surface tension

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