Characterising the infinite volume scaling limit of gradient models with non-convex energy

Abstract: 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 with respect to infinite volume Gibbs states for macroscopic functions on the continuum, 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 for non-convex energy complements recent studies in [Hil16, ABKM], as well as the proof for strictly convex Hamiltonians in [AW22].