Non-Perturbative Renormalization Group for the Diffusive Epidemic Process

Abstract

We consider the Diffusive Epidemic Process (DEP), a two-species reaction-diffusion process originally proposed to model disease spread within a population. This model exhibits a phase transition from an active epidemic to an absorbing state without sick individuals. Field-theoretic analyses suggest that this transition belongs to the universality class of Directed Percolation with a Conserved quantity (DP-C). However, some exact predictions derived from the symmetries of DP-C seem to be in contradiction with lattice simulations. Here we revisit the field theory of both DP-C and DEP. We discuss in detail the symmetries present in the various formulations of both models, some of which had not been identified previously. We then investigate the DP-C model using the derivative expansion of the non-perturbative renormalization group formalism. We recover previous results for DP-C near its upper critical dimension $d_c=4$, but show how the corresponding fixed point seems to no longer exist below $d\lesssim 3$. Consequences for the DEP universality class are considered.

arXiv comment12 pages, 2 figures, some corrections

References in corpus (28)

• Exact evolution equation for the effective potential
• Nonequilibrium Critical Phenomena and Phase Transitions into Absorbing States
• Non-Perturbative Renormalization Flow in Quantum Field Theory and Statistical Physics
• Universality classes in nonequilibrium lattice systems
• Exact Renormalization Group Equations. An Introductory Review
• Critical Exponents from the Effective Average Action
• Applications of Field-Theoretic Renormalization Group Methods to Reaction-Diffusion Problems
• Mind The Gap
• Wilson renormalization of a reaction-diffusion process
• Non Perturbative Renormalization Group study of reaction-diffusion processes and directed percolation
• General framework of the non-perturbative renormalization group for non-equilibrium steady states
• Non-perturbative fixed point in a non-equilibrium phase transition
• Critical behavior of a one-dimensional fixed-energy stochastic sandpile
• An exact mapping of the stochastic field theory for Manna sandpiles to interfaces in random media
• Quantitative Phase Diagrams of Branching and Annihilating Random Walks
• Frequency regulators for the nonperturbative renormalization group: A general study and the model A as a benchmark
• Field theories and exact stochastic equations for interacting particle systems
• Coherent-state path integral versus coarse-grained effective stochastic equation of motion: From reaction diffusion to stochastic sandpiles
• Diffusive epidemic process: theory and simulation
• Fully developed isotropic turbulence: symmetries and exact identities
• Critical behavior and conservation in directed sandpiles
• Finite scale singularity in the renormalization group flow of a reaction-diffusion system
• Comment on ``Critical behavior of a two-species reaction-diffusion problem''
• Could reggeon field theory be an effective theory for QCD in the Regge limit?
• Some exact results in branching and annihilating random walks
• The Abelian Manna model on two fractal lattices
• Directed Percolation with a Conserved Field and the Depinning Transition
• Reply to ``Comment on `Critical behavior of a two-species reaction-diffusion problem' ''

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