Crossover properties from random percolation to frustrated percolation

Abstract

We investigate the crossover properties of the frustrated percolation model on a two-dimensional square lattice, with asymmetric distribution of ferromagnetic and antiferromagnetic interactions. We determine the critical exponents nu, gamma and beta of the percolation transition of the model, for various values of the density of antiferromagnetic interactions pi in the range 0<pi<0.5. Our data are consistent with the existence of a crossover from random percolation behavior for pi=0, to frustrated percolation behavior, characterized by the critical exponents of the ferromagnetic 1/2-state Potts model, as soon as pi>0.