Decay of correlations in 1D lattice systems of continuous spins and long-range interaction
Abstract
We consider an one-dimensional lattice system of unbounded and continuous spins. The Hamiltonian consists of a perturbed strictly-convex single-site potential and with longe-range interaction. We show that if the interactions decay algebraically of order 2+a, a>0 then the correlations also decay algebraically of order 2+\~a for some \~a > 0. For the argument we generalize a method from Zegarlinski from finite-range to infinite-range interaction to get a preliminary decay of correlations, which is improved to the correct order by a recursive scheme based on Lebowitz inequalities. Because the decay of correlations yields the uniqueness of the Gibbs measure, the main result of this article yields that the on-phase region of a continuous spin system is at least as large as for the Ising model.
Keywords
Cite
@article{arxiv.1309.0857,
title = {Decay of correlations in 1D lattice systems of continuous spins and long-range interaction},
author = {Georg Menz and Robin Nittka},
journal= {arXiv preprint arXiv:1309.0857},
year = {2015}
}