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.
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The same transition is observed whether one fixes r and treats \(\Gamma/\Omega\) as a critical field, or whether one fixes \(\Gamma/\Omega\) and takes r to be the critical field. Here we adopt the latter, with \(\Gamma/\Omega=1\)
Observe that in this type of systems we do not have an exponential decay in the absorbing phase, but a power-law one, controlled asymptotically by the reaction \(A + A \to 0\)
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Received: 19 May 2003, Published online: 24 October 2003
PACS:
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
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Zhong, D., ben-Avraham, D. & Muñoz, M.A. Mean-field solution of the parity-conserving kinetic phase transition in one dimension. Eur. Phys. J. B 35, 505–511 (2003). https://doi.org/10.1140/epjb/e2003-00303-4
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DOI: https://doi.org/10.1140/epjb/e2003-00303-4