Continuous vs discrete spins in the hyperbolic plane
classification
🧮 math.PR
keywords
hyperbolicplaneboundaryconditionscontinuouscorrelationsdecaydiscrete
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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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