Scaling Limit of Some Gradient Systems 3 Theorem ( Brascamp - Lieb Inequalities )

We study the continuum scaling limit of some statistical mechanical models deened by convex Hamiltonians which are gradient perturbations of a massless free eld. By proving a central limit theorem for these models, we show that their long distance behavior is identical to a new (homogenized) continuum massless free eld. We shall also obtain some new bounds on the 2-point correlation functions of these models.