Crossover from Isotropic to Directed Percolation

Abstract

Directed percolation is one of the generic universality classes for dynamic processes. We study the crossover from isotropic to directed percolation by representing the combined problem as a random cluster model, with a parameter $r$ controlling the spontaneous birth of new forest fires. We obtain the exact crossover exponent $y_{DP}=y_T-1$ at $r=1$ using Coulomb gas methods in 2D. Isotropic percolation is stable, as is confirmed by numerical finite-size scaling results. For $D\ge 3$, the stability seems to change. An intuitive argument, however, suggests that directed percolation at $r=0$ is unstable and that the scaling properties of forest fires at intermediate values of $r$ are in the same universality class as isotropic percolation, not only in 2D, but in all dimensions.

4 pages, REVTeX, 4 epsf-emedded postscript figures

References in corpus (2)

• Are Damage Spreading Transitions Generically in the Universality Class of Directed Percolation?
• Crossover from Isotropic to Directed Percolation

Cited by in corpus (7)

• Nonequilibrium Critical Phenomena and Phase Transitions into Absorbing States
• Universality classes in nonequilibrium lattice systems
• Crossover from Isotropic to Directed Percolation
• Crossovers from parity conserving to directed percolation universality
• Finite-Size Scaling in Two-dimensional Continuum Percolation Models
• Crossover from dynamical percolation class to directed percolation class on a two dimensional lattice
• Critical and quasicritical behavior in a three-species dynamical model of semi-directed percolation