Percolation in a random environment.

Abstract

We consider bond percolation on the square lattice with perfectly correlated random probabilities. According to scaling considerations, mapping to a random walk problem and the results of Monte Carlo simulations the critical behavior of the system with varying degree of disorder is governed by new, random fixed points with anisotropic scaling properties. For weaker disorder both the magnetization and the anisotropy exponents are nonuniversal, whereas for strong enough disorder the system scales into an infinite randomness fixed point in which the critical exponents are exactly known.