Simple renormalization-group method for calculating geometrical equations of state

Abstract

We describe a real-space renormalization-group procedure to calculate geometrical equations of state for the entire range of values of the external parameters. Its use is as simple as a mean-field approximation; however, it yields nontrivial results and can be systematically improved. We illustrate it by calculating, for all bond concentrations, the site mass density for the complete and the backbone percolating infinite clusters in square lattice: the results are quite satisfactory.