Scaling limit and convergence of smoothed covariance for gradient models with non-convex potential
Abstract
A discrete gradient model for interfaces is studied. The interaction potential is a non-convex perturbation of the quadratic gradient potential. Based on a representation for the finite volume Gibbs measure obtained via a renormalization group analysis by Adams, Kotecký and Müller in [AKM] it is proven that the scaling limit is a continuum massless Gaussian free field. From probabilistic point of view, this is a Central Limit Theorem for strongly dependent random fields. Additionally, the convergence of covariances, smoothed on a scale smaller than the system size, is proven.
- Publication:
-
arXiv e-prints
- Pub Date:
- March 2016
- DOI:
- 10.48550/arXiv.1603.04703
- arXiv:
- arXiv:1603.04703
- Bibcode:
- 2016arXiv160304703H
- Keywords:
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- Mathematical Physics;
- Mathematics - Probability;
- 60F05 (Primary);
- 82B20 (Secondary)