Complete Analyticity of the 2D Potts Model above the Critical Temperature
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We investigate the complete analyticity (CA) of the two-dimensional q-state Potts model for large values of q. We are able to prove it for every temperature \(\), provided we restrict ourselves to nice subsets, their niceness depending on the temperature T. Contrary to this restricted complete analyticity (RCA), the full CA is known to fail for some values of the temperature above \(\).
Our proof is based on Pirogov-Sinai theory and cluster expansions for the Fortuin-Kasteleyn representation, which are available for the Potts model at all temperatures, provided q is large enough.
KeywordsCritical Temperature Potts Model Complete Analyticity Cluster Expansion
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