Homology of Fortuin-Kasteleyn clusters of Potts models on the torus
arXiv:hep-th/0111193 · doi:10.1023/A:1019979326380
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 what seems logarithmic corrections makes it harder to decide.
12 pages, 2 figures, submitted to J. Stat. Phys
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