97-34 van Enter A.-C.-D., Fern\'andez R., Schonmann R.-H., Shlosman S.-B.

Complete Analyticity of the Potts model above the critical temperature. (76K, amstex) Jan 27, 97

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Abstract. We investigate the complete analyticity of the two-dimensional q-state Potts model for large values of q. We are able to prove it for every temperature T > T_{cr}, 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 T_{cr}(q). 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.

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