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Continuous vs discrete spins in the hyperbolic plane

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arxiv 1609.09040 v3 pith:O3BKR2TB submitted 2016-09-28 math.PR

Itai Benjamini , Gady Kozma This is my paper · ORCID
classification math.PR
keywords hyperbolicplaneboundaryconditionscontinuouscorrelationsdecaydiscrete
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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 $n>1$.

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