Active Width at a Slanted Active Boundary in Directed Percolation

Details Active Width at a Slanted Active Boundary in Directed Percolation Active Width at a Slanted Active Boundary in Directed Percolation

1999-04-28

arxiv.org/abs/cond-mat/9904417v1

Phys. Rev. E 60, 2496 (1999)

Physics

Condensed Matter

Statistical Mechanics

5 pages, 5 figures

Scientific paper

10.1103/PhysRevE.60.2496

The width W of the active region around an active moving wall in a directed percolation process diverges at the percolation threshold p_c as W \simeq A \epsilon^{-\nu_\parallel} \ln(\epsilon_0/\epsilon), with \epsilon=p_c-p, \epsilon_0 a constant, and \nu_\parallel=1.734 the critical exponent of the characteristic time needed to reach the stationary state \xi_\parallel \sim \epsilon^{-\nu_\parallel}. The logarithmic factor arises from screening of statistically independent needle shaped sub clusters in the active region. Numerical data confirm this scaling behaviour.

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