Non-universal critical initial slip of parity conserving branching and annihilating random walkers with long-range diffusion

F.C. dos Anjos, Iram Gléria, M.L. Lyra and C. Argolo

Physica A: Statistical Mechanics and its Applications, 2020, vol. 549, issue C

Abstract: We consider a parity conserving model of branching and annihilating random walkers with long-range diffusion. We follow the short-time dynamics at the critical region to obtain the set of critical exponents associated to the growth in the number particles and its fluctuations, as well as the critical second-order moment ratio. Diffusion and branching processes are controlled by a diffusion probability p and the flight distance follows a Lévy distribution with exponent α. Three short-time scaling regimes are identified as a function of the Lévy exponent. For α≤5∕2 infinitesimal branching is relevant and leads to a finite density of walkers. An absorbing-state dynamic phase transition takes place at a finite branching probability for α>5∕2. Short-range power-law scaling occurs for α≥7∕2. In the intermediate regime, continuously varying exponents are obtained with the second-order cumulant depicting a non-monotonous behavior. The relative influence of Lévy diffusion and branching on the critical diffusion probability is also discussed.

Keywords: Non-equilibrium transition; Parity-Conserving; Lévy-flight; Critical dynamics (search for similar items in EconPapers)
Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:549:y:2020:i:c:s0378437120301072

DOI: 10.1016/j.physa.2020.124325

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