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 EP(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 Ep(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.