Percolation, clusters, and properties of a dilute Potts model

It is shown that the partition function of a dilute q-state Potts model (DQPM), in which any lattice site may be vacant, may be written as the generating function of a q-state site-bond-correlated percolation model (QSBCPM). Based on such a connection, we define an interaction factor I, a nonpercolating geometrical factor gf, and a percolating geometrical factor gₚ, where I is a simple function of the normalized chemical potential and coupling constants of the DQPM and gf and gₚ depend only on the geometrical properties of the lattice. The thermal properties of the DQPM may be derived from I, gf, and gₚ. The theory is confirmed by exact calculations for one-dimensional DQPM. The connection between the DQPM and the QSBCPM may be used to formulate the percolation renormalization group and the percolation Monte Carlo studies of the DQPM.