English

Continuous vs discrete spins in the hyperbolic plane

Probability 2017-06-19 v3

Abstract

We study the O(n)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>1n>1.

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

R2 v1 2026-06-22T16:04:29.911Z