Towards Classification of Phase Transitions in Reaction--Diffusion Models

Abstract

Equilibrium phase transitions are associated with rearrangements of minima of a (Lagrangian) potential. Treatment of non-equilibrium 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 RG transformations.

14 pages, 9 figures

References in corpus (52)

• Nonequilibrium Critical Phenomena and Phase Transitions into Absorbing States
• Universality classes in nonequilibrium lattice systems
• Critical Coarsening without Surface Tension: the Voter Universality Class
• Universal scaling behavior of non-equilibrium phase transitions
• Applications of Field-Theoretic Renormalization Group Methods to Reaction-Diffusion Problems
• Theory of Branching and Annihilating Random Walks
• Renormalization Group Calculation for the Reaction $kA\to \varnothing$
• Rare Events Statistics in Reaction--Diffusion Systems
• The universality class of absorbing phase transitions with a conserved field
• Field Theory of Branching and Annihilating Random Walks
• The Field Theory Approach to Percolation Processes
• Renormalization Group Study of the A+B->0 Diffusion-Limited Reaction
• Integration of Langevin Equations with Multiplicative Noise and Viability of Field Theories for Absorbing Phase Transitions
• A Generalized Epidemic Process and Tricritical Dynamic Percolation
• Generalized Scaling for Models with Multiple Absorbing States
• Langevin description of critical phenomena with two symmetric absorbing states
• `Real' vs `Imaginary' Noise in Diffusion-Limited Reactions
• Non Perturbative Renormalization Group study of reaction-diffusion processes and directed percolation
• Fluctuation Statistics in Networks: a Stochastic Path Integral Approach
• Critical properties of the reaction - diffusion model 2A -> 3A, 2A ->0
• Non-perturbative fixed point in a non-equilibrium phase transition
• Absorbing Phase Transitions of Branching-Annihilating Random Walks
• The non-equilibrium phase transition of the pair-contact process with diffusion
• Quantitative Phase Diagrams of Branching and Annihilating Random Walks
• Universality Class of Two-Offspring Branching Annihilating Random Walks
• Pair contact process with diffusion - A new type of nonequilibrium critical behavior?
• Survival probability of a diffusing particle in the presence of Poisson-distributed mobile traps
• Tricritical directed percolation
• Novel universality class of absorbing transitions with continuously varying critical exponents
• Exact solution of a reaction-diffusion process with three-site interactions
• Universality class of nonequilibrium phase transitions with infinitely many-absorbing-states
• Universal scaling behavior at the upper critical dimension of non-equilibrium continuous phase transitions
• On the critical behavior of the one dimensional, diffusive pair contact process
• Nonuniversality in the pair contact process with diffusion
• Universal finite-size scaling amplitudes in anisotropic scaling
• Pair Contact Process with Diffusion: Failure of Master Equation Field Theory
• Binary spreading process with parity conservation
• Scaling behavior of the order parameter and its conjugated field in an absorbing phase transition around the upper critical dimension
• Splitting the voter criticality
• Universality in the pair contact process with diffusion
• Phase transition of a two dimensional binary spreading model
• The phase transition of the diffusive pair contact process revisited
• Local scale-invariances in the bosonic contact and pair-contact processes
• Phase transition in a triplet process
• Phase transitions and correlations in the bosonic pair contact process with diffusion: Exact results
• Scaling behavior of the directed percolation universality class
• Cluster mean-field approximations with the coherent-anomaly-method analysis for the driven pair contact process with diffusion
• Generating function, path integral representation, and equivalence for stochastic exclusive particle systems
• Critical behavior of nonequilibrium models with infinitely many absorbing states
• Revisiting the nonequilibrium phase transition of the triplet-creation model
• The role of diffusion in branching and annihilation random walk models
• Critical behavior in reaction-diffusion systems exhibiting absorbing phase transition

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