  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].
