Absorbing Phase Transitions of Branching-Annihilating Random Walks

2002/08/26 by Julien Kockelkoren, Hugues Chaté · 5 citations
Materials Science · Mathematics · Physics and Astronomy · #Branching (polymer chemistry) #Force Microscopy Techniques and Applications #Material Dynamics and Properties #Materials science #Mathematics #Phase transition #Physics #Quantum mechanics #Random walk #Statistical physics #Statistics #Theoretical and Computational Physics #cond-mat.stat-mech

paper · pdf · doi:10.1103/physrevlett.90.125701

4 pages, 4 figures

arxiv created 2002/08/26 · openalex publication_date 2003/03/26 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

The phase transitions to absorbing states of the branching-annihilating reaction-diffusion processes mA-->(m+k)A, nA-->(n-l)A are studied systematically in one space dimension within a new family of models. Four universality classes of nontrivial critical behavior are found. This provides, in particular, the first evidence of universal scaling laws for pair and triplet processes.

Citations

• Non-equilibrium critical phenomena and phase transitions into absorbing states
• Critical properties of the reaction-diffusion model2A→3A,2A→0
• Cyclically coupled spreading and pair annihilation
• Critical Exponents for Branching Annihilating Random Walks with an Even Number of Offspring

Cited by

• Universality-class crossover by a nonorder field introduced to the pair contact process with diffusion
• Critical study of the absorbing phase transition in a four-state predator–prey model in one dimension
• Critical decay exponent of the pair contact process with diffusion
• Generalized scaling relations for unidirectionally coupled nonequilibrium systems
• Moment ratios for the pair-contact process with diffusion