Scaling functions of the q-state Potts model on planar lattices

Based on the subgraph expansion of the q -state Potts model (QPM) in an external field, it has been shown that the QPM is corresponding to a q -state bond-correlated percolation model (QBCPM). The histogram Monte Carlo simulation method proposed by Hu is used to calculate the existence probability E P ( G, p, q and the percolation probability P(G, p, q) of the QBCPM on the honeycomb, the Kagome, and the plane triangular lattices with various linear dimensions. From E p ( G, p, q ) and P(G, p, q ) we obtain scaling functions of the QPM and QBCPM. We find that as q or the coordination number of the lattices increases, the widths of the scaling functions also increase. The implication of this study is discussed.