Crossover from Isotropic to Directed Percolation

Details Crossover from Isotropic to Directed Percolation Crossover from Isotropic to Directed Percolation

1996-09-30

arxiv.org/abs/cond-mat/9609287v1

Phys. Rev. Lett. 78, 1850 (1997)

Physics

Condensed Matter

4 pages, REVTeX, 4 epsf-emedded postscript figures

Scientific paper

10.1103/PhysRevLett.78.1850

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 $D \geq 3$, 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.

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