Site Percolation in a Square Lattice with Second- and Dilute First-Neighbor Bonds

A two-parameter real-space renormalization-group approach to the site-percolation problem in a square lattice is proposed. The two parameters are the concentration p of active first-neighbor bonds, and the concentration q of occupied sites. From these two parameters one can calculate two independent critical exponents, and the others can be obtained through scaling relations, with no need of external applied fields.