Geometrical factor and thermal properties of a sublattice dilute Potts model

Based on the connection between a sublattice dilute q-state Potts model (SDQPM) and a correlated percolation model, we define a nonpercolating geometrical factor $g_f$ and a percolating geometrical factor $g_p$, which depend only on q and geometrical properties of the system. The thermal properties of the SDQPM may be derived simply from $g_f$ and $g_p$. The theory is confirmed by an exact calculation for one-dimensional SDQPM and may be extended to other interacting systems.