Continuous vs discrete spins in the hyperbolic plane

Abstract

We study the $O(n)$ model on graphs quasi-isometric to the hyperbolic plane, with free boundary conditions. We observe that the pair correlations decay exponentially with distance, for all temperatures, if and only if $n>1$.

4 pages. New version strengthens the result a little and adds references to all necessary background material. To appear in Journal of Statistical Physics

References in corpus (1)

• Percolation in the Hyperbolic Plane