Document 
Eur. Phys. J. B 35, 505-511 (2003)
DOI: 10.1140/epjb/e2003-00303-4
Mean-field solution of the parity-conserving kinetic phase transition in one dimension
D. Zhong1, D. ben-Avraham1 and M.A. Muñoz21 Department of Physics, Clarkson University, Postdam, New York 13699-5820 USA
2 Instituto de Física Teórica y Computacional Carlos I and Departamento de Electromagnetismo y Física de la Materia, Facultad de Ciencias, Universidad de Granada, 18071 Granada, Spain
mamunoz@onsager.ugr.es
(Received 19 May 2003 Published online 24 October 2003)
Abstract
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 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.
02.50.Ey - Stochastic processes.
05.50.+q - Lattice theory and statistics (Ising, Potts, etc.).
05.70.Ln - Nonequilibrium and irreversible thermodynamics.
82.40.-g - Chemical kinetics and reactions: special regimes and techniques .
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag 2003