Continuous vs discrete spins in the hyperbolic plane
Probability
2017-06-19 v3
Abstract
We study the 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 .
Keywords
Cite
@article{arxiv.1609.09040,
title = {Continuous vs discrete spins in the hyperbolic plane},
author = {Itai Benjamini and Gady Kozma},
journal= {arXiv preprint arXiv:1609.09040},
year = {2017}
}
Comments
4 pages. New version strengthens the result a little and adds references to all necessary background material. To appear in Journal of Statistical Physics