Classification of phase transitions in reaction-diffusion models

2006/05/31 by Vlad Elgart, Alex Kamenev · 2 citations
Biochemistry, Genetics and Molecular Biology · Materials Science · Physics and Astronomy · #Material Dynamics and Properties #Protein Structure and Dynamics #Theoretical and Computational Physics #cond-mat.stat-mech #q-bio.PE

paper · pdf · doi:10.1103/physreve.74.041101

published as Phys. Rev. E 74, 041101 (2006) · 14 pages, 9 figures

openalex publication_date 2006/10/02 · arxiv created 2006/10/12 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Equilibrium phase transitions are associated with rearrangements of minima of a (Lagrangian) potential. Treatment of nonequilibrium systems requires doubling of degrees of freedom, which may be often interpreted as a transition from the "coordinate"- to the "phase"-space representation. As a result, one has to deal with the Hamiltonian formulation of the field theory instead of the Lagrangian one. We suggest a classification scheme of phase transitions in reaction-diffusion models based on the topology of the phase portraits of corresponding Hamiltonians. In models with an absorbing state such a topology is fully determined by intersecting curves of zero "energy." We identify four families of topologically distinct classes of phase portraits stable upon renormalization group transformations.

Citations

• Nonperturbative Fixed Point in a Nonequilibrium Phase Transition
• Langevin Description of Critical Phenomena with Two Symmetric Absorbing States
• Nonequilibrium Critical Phenomena and Phase Transitions into Absorbing States
• The non-equilibrium phase transition of the pair-contact process with diffusion
• Cluster mean-field approximations with the coherent-anomaly-method analysis for the driven pair contact process with diffusion

Cited by

• Aging processes in reversible reaction-diffusion systems
• Local scale invariance in the parity conserving non-equilibrium kinetic Ising model