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Reflection Positivity of the Random-Cluster Measure Invalidated for Noninteger q

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Abstract

We consider the random-cluster Potts measure on a lattice torus that weights each connected component by a positive number q. We show, by constructing a counterexample, that this measure is not reflection-positive unless q is integer.

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Authors and Affiliations

  1. Mathematisch Instituut, KUN, 6525 ED, Nijmegen, The Netherlands

    Marek Biskup

  2. Department of Theoretical Physics, MFF, Charles University, 180 00, Prague, Czech Republic

    Marek Biskup

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  1. Marek Biskup
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Biskup, M. Reflection Positivity of the Random-Cluster Measure Invalidated for Noninteger q . Journal of Statistical Physics 92, 369–375 (1998). https://doi.org/10.1023/A:1023076202262

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  • DOI: https://doi.org/10.1023/A:1023076202262

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