No phase transition for Gaussian fields with bounded spins

PABLO A. FERRARI; SEBASTIAN P. GRYNBERG

JOURNAL OF STATISTICAL PHYSICS

SPRINGER

Año: 2008 p. 195 - 202

0022-4715

Let a<b, Omega=[a,b]^{Z^d} and H be the (formal) Hamiltonian defined on Omega by  H(eta) = rac12 sum_{x,yinZ^d} J(x-y) (eta(x)-eta(y))^2 where J:Z^d oR is any summable non-negative symmetric function (J(x)ge 0 for all xinZ^d, sum_x J(x)<infty and J(x)=J(-x)). We prove that there is a unique Gibbs measure on Omega associated to H. The result is a consequence of the fact that the corresponding Gibbs sampler is attractive and has a unique invariant measure.