No phase transition for Gaussian fields with bounded spins
arXiv:0706.3714 · doi:10.1007/s10955-007-9423-9
Abstract
Let a<b, Ω=[a,b]^{\Z^d} and H be the (formal) Hamiltonian defined on Ωby H(η) = \frac12 \sum_{x,y\in\Z^d} J(x-y) (η(x)-η(y))^2 where J:\Z^d\to\R is any summable non-negative symmetric function (J(x)\ge 0 for all x\in\Z^d, \sum_x J(x)<\infty and J(x)=J(-x)). We prove that there is a unique Gibbs measure on Ωassociated to H. The result is a consequence of the fact that the corresponding Gibbs sampler is attractive and has a unique invariant measure.
7 pages