The Hessian of surface tension characterises scaling limit of gradient models with non-convex energy
- Resource Type
- Working Paper
- Authors
- Adams, Stefan; Koller, Andreas
- Source
- Subject
- Mathematics - Probability
Mathematical Physics
60K35, 82B20, 82B28
- Language
We study the scaling limit of statistical mechanics models with non-convex Hamiltonians that are gradient perturbations of Gaussian measures. Characterising features of our gradient models are the imposed boundary tilt and the surface tension (free energy) as a function of tilt. In the regime of low temperatures and bounded tilt, we prove the scaling limit for macroscopic functions on the torus, and we show that the limit is a continuum Gaussian Free Field with covariance (diffusion) matrix given as the Hessian of surface tension. Our proof of this longstanding conjecture complements recent studies in [Hil16], [ABKM].