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Homology of Fortuin–Kasteleyn Clusters of Potts Models on the Torus

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Abstract

Topological properties of Fortuin–Kasteleyn clusters are studied on the torus. Namely, the probability that their topology yields a given subgroup of the first homology group of the torus is computed for Q=1, 2, 3 and 4. The expressions generalize those obtained by Pinson for percolation (Q=1). Numerical results are also presented for three tori of different moduli. They agree with the theoretical predictions for Q=1, 2 and 3. For Q=4 agreement is not ruled out but logarithmic corrections are probably present and they make it harder to decide.

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  1. Département de Physique, Université de Montréal, Case Postale 6128, succ. centre-ville, Montréal, Québec, Canada, H3C 1J7

    Louis-Pierre Arguin

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  1. Louis-Pierre Arguin
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Arguin, LP. Homology of Fortuin–Kasteleyn Clusters of Potts Models on the Torus. Journal of Statistical Physics 109, 301–310 (2002). https://doi.org/10.1023/A:1019979326380

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  • DOI: https://doi.org/10.1023/A:1019979326380

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