Non Perturbative Renormalization Group study of reaction-diffusion processes and directed percolation

Abstract

We investigate non-equilibrium critical phenomena using a nonperturbative renormalization group method. Reaction-diffusion processes are described by a scale dependent effective action which evolution is governed by very generic flow equations, that are derived. They allow to recover the critical exponents of directed percolation, and moreover to calculate the microscopic reaction rates which give rise to a phase transition in the case of branching and annihilating random walks with odd number of offsprings, even in three dimensions.

4 pages, 1 figure, published version (discussion and figure modified)

References in corpus (1)

• Optimization of the derivative expansion in the nonperturbative renormalization group

Cited by in corpus (80)

• The nonperturbative functional renormalization group and its applications
• Keldysh Field Theory for Driven Open Quantum Systems
• An Introduction to the Nonperturbative Renormalization Group
• Applications of Field-Theoretic Renormalization Group Methods to Reaction-Diffusion Problems
• The Field Theory Approach to Percolation Processes
• Non-perturbative renormalization group for the Kardar-Parisi-Zhang equation
• Integration of Langevin Equations with Multiplicative Noise and Viability of Field Theories for Absorbing Phase Transitions
• Convergence of Non-Perturbative Approximations to the Renormalization Group
• Nonthermal fixed points and the functional renormalization group
• Langevin description of critical phenomena with two symmetric absorbing states
• Master equations and the theory of stochastic path integrals
• Functional renormalization group for non-equilibrium quantum many-body problems
• Non-perturbative renormalisation group for the Kardar-Parisi-Zhang equation: general framework and first applications
• Real time correlation functions and the functional renormalisation group
• Non-perturbative renormalization group preserving full-momentum dependence: implementation and quantitative evaluation
• Functional renormalisation group approach to far-from-equilibrium quantum field dynamics
• General framework of the non-perturbative renormalization group for non-equilibrium steady states
• Non-perturbative fixed point in a non-equilibrium phase transition
• Nonperturbative renormalization group for the stationary Kardar-Parisi-Zhang equation: scaling functions and amplitude ratios in 1+1, 2+1 and 3+1 dimensions
• Fully developed isotropic turbulence: nonperturbative renormalization group formalism and fixed point solution
• Ultracold atoms and the Functional Renormalization Group
• Quantitative Phase Diagrams of Branching and Annihilating Random Walks
• Non-perturbative Approach to Critical Dynamics
• Large deviations and dynamical phase transitions in stochastic chemical networks
• Towards Classification of Phase Transitions in Reaction--Diffusion Models
• Universality in driven open quantum matter
• Introduction to the nonequilibrium functional renormalization group
• Analytic continuation of functional renormalization group equations
• Quantum dynamical field theory for non-equilibrium phase transitions in driven open systems
• Far-from-equilibrium quantum many-body dynamics
• Surprises in the $O(N)$ models: nonperturbative fixed points, large $N$ limit and multi-criticality
• Frequency regulators for the nonperturbative renormalization group: A general study and the model A as a benchmark
• Phenomenology of a First Order Dark State Phase Transition
• Optimization of field-dependent nonperturbative renormalization group flows
• From quantum to classical dynamics: The relativistic $O(N)$ model in the framework of the real-time functional renormalization group
• Why Might the Standard Large $N$ Analysis Fail in the O($N$) Model: The Role of Cusps in the Fixed Point Potentials
• Effects of turbulent mixing on the nonequilibrium critical behaviour
• Universal short-time dynamics: boundary functional renormalization group for a temperature quench
• Bound states of the ${\varphi }^4$ model via the nonperturbative renormalization group
• Conformal invariance in the nonperturbative renormalization group: a rationale for choosing the regulator
• Breaking of scale invariance in the time dependence of correlation functions in isotropic and homogeneous turbulence
• Non-Perturbative Renormalization Group for Simple Fluids
• Reaction-diffusion processes and non-perturbative renormalisation group
• Ultracold gases far from equilibrium
• Finite scale singularity in the renormalization group flow of a reaction-diffusion system
• KPZ equation with short-range correlated noise: emergent symmetries and non-universal observables
• The finite $N$ origin of the Bardeen-Moshe-Bander phenomenon and its extension at $N=\infty$ by singular fixed points
• Stationary, isotropic and homogeneous two-dimensional turbulence: a first non-perturbative renormalization group approach
• Kardar-Parisi-Zhang Equation with temporally correlated noise: a non-perturbative renormalization group approach
• Non-Perturbative Renormalization Group for the Diffusive Epidemic Process
• Non-universality in the erosion of tilted landscapes
• On the Validity of the Law of Mass Action in Three-Dimensional Coagulation Processes
• Non-equilibrium time evolution of bosons from the functional renormalization group
• Strong-coupling phases of the anisotropic Kardar-Parisi-Zhang equation
• Could reggeon field theory be an effective theory for QCD in the Regge limit?
• Some exact results in branching and annihilating random walks
• Field-theoretic analysis of directed percolation: Three-loop approximation
• Branching rate expansion around annihilating random walks
• The role of diffusion in branching and annihilation random walk models
• Network Renormalization
• Novel critical phenomena in compressible polar active fluids: Dynamical and Functional Renormalization Group Studies
• Conformal invariance and composite operators: A strategy for improving the derivative expansion of the nonperturbative renormalization group
• Critical behavior of the two dimensional 2A->3A, 4A->0 binary system
• The $q-$state Potts model from the Nonperturbative Renormalization Group
• Background Field Functional Renormalization Group for Absorbing State Phase Transitions
• Long-Range and Many-Body Effects in Coagulation Processes
• Single-site approximation for reaction-diffusion processes
• Incompleteness of the large-$N$ analysis of the $O(N)$ models: Nonperturbative cuspy fixed points and their nontrivial homotopy at finite $N$
• Population Dynamics of Schrödinger Cats
• Fluctuation Effects in the Pair-Annihilation Process with Lévy Dynamics
• Functional Renormalisation Group for Brownian Motion I: The Effective Equations of Motion
• Identifying universality classes of absorbing phase transitions by block renormalization
• Coarse-graining in time with the Functional Renormalisation Group: Relaxation in Brownian Motion
• Instability of the engineered dark state in two-band fermions under number-conserving dissipative dynamics
• Phase transitions in in vivo or in vitro populations of spiking neurons belong to different universality classes
• A fixed point can hide another one: the nonperturbative behavior of the tetracritical fixed point of the O($N$) models at large $N$
• On the maximal noise for stochastic and QCD traveling waves
• Influence of turbulent mixing on critical behavior of directed percolation process : effect of compressibility
• Path integral evaluation of the one-loop effective potential in field theory of diffusion-limited reactions
• Phase diagram of Model C in the parametric space of order parameter and space dimensions