Communications in Mathematical Physics

, Volume 189, Issue 2, pp 373–393 | Cite as

Complete Analyticity of the 2D Potts Model above the Critical Temperature

  • Aernout C. D. van Enter
  • Roberto Fernández
  • Roberto H. Schonmann
  • Senya B. Shlosman

Abstract:

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.

Keywords

Critical Temperature Potts Model Complete Analyticity Cluster Expansion 

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Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Aernout C. D. van Enter
    • 1
  • Roberto Fernández
    • 2
  • Roberto H. Schonmann
    • 3
  • Senya B. Shlosman
    • 4
  1. 1.Instituut voor Theoretische Natuurkunde, Rijksuniversiteit Groningen, 9747 AG Groningen, The NetherlandsNL
  2. 2.Instituto de Matemática e Estatística, Universidade de São Paulo, Caixa Postal 66281, 05389-970 Sáo Paulo, BrazilBR
  3. 3.Mathematics Department, University of California at Los Angeles, Los Angeles, CA 90024, USAUS
  4. 4.Mathematics Department, University of California at Irvine, Irvine, CA 92717, USAUS

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