Crossover properties from random percolation to frustrated percolation

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 n in the range 0 less than or equal to pi less than or equal to 0.5. Our data is 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.