Homology of Fortuin-Kasteleyn clusters of Potts models on the torus

Details Homology of Fortuin-Kasteleyn clusters of Potts models on the torus Homology of Fortuin-Kasteleyn clusters of Potts models on the torus

2001-11-21

arxiv.org/abs/hep-th/0111193v2

J.Statist.Phys.109:301-310,2002

Physics

High Energy Physics

High Energy Physics - Theory

12 pages, 2 figures, submitted to J. Stat. Phys

Scientific paper

10.1023/A:1019979326380

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 what seems logarithmic corrections makes it harder to decide.

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