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Journal of Statistical Physics

, Volume 109, Issue 1–2, pp 301–310 | Cite as

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

  • Louis-Pierre Arguin
Article

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.

Potts models bond percolation torus 

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Copyright information

© Plenum Publishing Corporation 2002

Authors and Affiliations

  • Louis-Pierre Arguin
    • 1
  1. 1.Département de PhysiqueUniversité de MontréalMontréalCanada

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