Scaling limit for a class of gradient fields with nonconvex potentials
Scaling limit for a class of gradient fields with nonconvex potentials
We consider gradient fields (ϕx : x∈ℤd) whose law takes the Gibbs–Boltzmann form Z−1exp{−∑〈x, y〉V(ϕy−ϕx)}, where the sum runs over nearest neighbors. We assume that the potential V admits the representation V(η):=−log∫ϱ(d κ)exp[−½κη2], where ϱ is a positive measure with compact support in (0, ∞). Hence, the potential V is …