Percolation renormalization-group calculations of equations of state for the Potts model

The connection between the q-state Potts model (QPM) and a q-state bond-correlated percolation model (QBCPM) has been used to formulate a percolation renormalization group method (PRGM) for calculating the free energy, the critical point pc, and critical exponents for the QPM. In this paper the PRGM is extended to calculate the percolation probability P, the backbone mass density PB, and the backbone fractal dimensions DB for the QBCPM and the QPM on the square lattice.