Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2003-04-21
Physics
Condensed Matter
Statistical Mechanics
4 Figures. 9 Pages. revtex4. Some comments have been improved
Scientific paper
10.1140/epjb/e2003-00303-4
A two-offspring branching annihilating random walk model, with finite reaction rates, is studied in one-dimension. The model exhibits a transition from an active to an absorbing phase, expected to belong to the $DP2$ universality class embracing systems that possess two symmetric absorbing states, which in one-dimensional systems, is in many cases equivalent to parity conservation. The phase transition is studied analytically through a mean-field like modification of the so-called {\it parity interval method}. The original method of parity intervals allows for an exact analysis of the diffusion-controlled limit of infinite reaction rate, where there is no active phase and hence no phase transition. For finite rates, we obtain a surprisingly good description of the transition which compares favorably with the outcome of Monte Carlo simulations. This provides one of the first analytical attempts to deal with the broadly studied DP2 universality class.
ben-Avraham Daniel
Munoz Miguel A.
Zhong Dexin
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