Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2002-07-08
J. Phys. A35, 7983 (2002)
Physics
Condensed Matter
Statistical Mechanics
12 pages, 4 figures
Scientific paper
10.1088/0305-4470/35/38/302
We study a version of compact directed percolation (CDP) in one dimension in which occupation of a site for the first time requires that a "mine" or antiparticle be eliminated. This process is analogous to the variant of directed percolation with a long-time memory, proposed by Grassberger, Chate and Rousseau [Phys. Rev. E 55, 2488 (1997)] in order to understand spreading at a critical point involving an infinite number of absorbing configurations. The problem is equivalent to that of a pair of random walkers in the presence of movable partial reflectors. The walkers, which are unbiased, start one lattice spacing apart, and annihilate on their first contact. Each time one of the walkers tries to visit a new site, it is reflected (with probability r) back to its previous position, while the reflector is simultaneously pushed one step away from the walker. Iteration of the discrete-time evolution equation for the probability distribution yields the survival probability S(t). We find that S(t) \sim t^{-delta}, with delta varying continuously between 1/2 and 1.160 as the reflection probability varies between 0 and 1.
ben-Avraham Daniel
Dickman Ronald
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