Percolation in 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 non-universal, whereas for strong enough disorder the system scales into an {\it infinite randomness fixed point} in which the critical exponents are exactly known.

8 pages, 7 figures

References in corpus (4)

• Exact renormalization of the random transverse-field Ising spin chain in the strongly ordered and strongly disordered Griffiths phases
• Disorder induced cross-over effects at quantum critical points
• Strongly disordered spin ladders
• Surface-induced disorder and aperiodic perturbations at first-order transitions

Cited by in corpus (6)

• Rare region effects at classical, quantum, and non-equilibrium phase transitions
• Strong disorder RG approach of random systems
• Absorbing state phase transitions with quenched disorder
• Infinite-randomness criticality in monitored quantum dynamics with static disorder
• Percolation in Media with Columnar Disorder
• Density of critical clusters in strips of strongly disordered systems