Histogram Monte Carlo approach to thermal properties of the Potts model on planar lattices

Based on the connection between the q-state Potts model (QPM) and a q-state bond-correlated percolation model (QBCPM), we use the histogram Monte Carlo simulation method to calculate the free energy Fe, the internal energy U, and the specific heat Ch of the QPM on the honeycomb, the square, the Kagome, and the plane triangular lattices and for q being 2–5, where q = 2 corresponds to the Ising model. Our results for the Ising model agree very well with exact results for thermodynamic systems when the temperature is away from the critical temperature.