Pair Contact Process with Diffusion: Failure of Master Equation Field Theory

Abstract

We demonstrate that the `microscopic' field theory representation, directly derived from the corresponding master equation, fails to adequately capture the continuous nonequilibrium phase transition of the Pair Contact Process with Diffusion (PCPD). The ensuing renormalization group (RG) flow equations do not allow for a stable fixed point in the parameter region that is accessible by the physical initial conditions. There exists a stable RG fixed point outside this regime, but the resulting scaling exponents, in conjunction with the predicted particle anticorrelations at the critical point, would be in contradiction with the positivity of the equal-time mean-square particle number fluctuations. We conclude that a more coarse-grained effective field theory approach is required to elucidate the critical properties of the PCPD.

revtex, 8 pages, 1 figure included

References in corpus (24)

• Nonequilibrium Critical Phenomena and Phase Transitions into Absorbing States
• Universality classes in nonequilibrium lattice systems
• Theory of Branching and Annihilating Random Walks
• Renormalization Group Calculation for the Reaction $kA\to \varnothing$
• Field Theory of Branching and Annihilating Random Walks
• `Real' vs `Imaginary' Noise in Diffusion-Limited Reactions
• Critical properties of the reaction - diffusion model 2A -> 3A, 2A ->0
• Absorbing Phase Transitions of Branching-Annihilating Random Walks
• The non-equilibrium phase transition of the pair-contact process with diffusion
• Pair contact process with diffusion - A new type of nonequilibrium critical behavior?
• Critical behaviour of the 1d annihilation fission process 2A->0, 2A->3A
• Novel universality class of absorbing transitions with continuously varying critical exponents
• 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
• Cyclically coupled spreading and pair annihilation
• Binary spreading process with parity conservation
• Phase transition of a two dimensional binary spreading model
• Universality in the pair contact process with diffusion
• Phase transition of the one-dimensional coagulation-production process
• Phase transition classes in triplet and quadruplet reaction diffusion models
• Phase transition in a triplet process
• Stochastic cellular automaton for the coagulation-fission-process 2A->3A, 2A->A
• Roughening transition driven by a binary spreading process

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• Ageing without detailed balance in the bosonic contact and pair-contact processes: exact results
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• A fixed point can hide another one: the nonperturbative behavior of the tetracritical fixed point of the O($N$) models at large $N$
• The phase transition of triplet reaction-diffusion models
• Universality-class crossover by a nonorder field introduced to the pair contact process with diffusion