Monte Carlo study of the Potts model on the square and the simple cubic lattices

It has been shown that the partition function of the q-state Potts model (QPM) is the generating function of a q-state bond-correlated percolation model (QBCPM) such that the spontaneous magnetization M, the magnetic susceptibility χ, the internal energy U, and the specific heat $C_h$ for the QPM are related to the percolation probability P, the mean cluster size S, the average number of occupied bond p¯, and the fluctuations of occupied bonds F for the QBCPM. We use the Monte Carlo simulation method of Swendsen and Wang and the multiple labeling technique of Hoshen and Kopelman to calculate P, S, p¯, and F for the QBCPM on the square and the simple cubic lattice. Our calculations give accurate critical points for the QPM.