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

@inproceedings{ArguinHomologyOF,
title={Homology of Fortuin-Kasteleyn clusters of Potts models on the torus},
author={Louis-Pierre Arguin}
}

Louis-Pierre Arguin

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… CONTINUE READING