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

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

2004-08-03

arxiv.org/abs/cond-mat/0408064v2

Phys. Rev. E 70 (2004) 056114

Physics

Condensed Matter

Statistical Mechanics

revtex, 8 pages, 1 figure included

Scientific paper

10.1103/PhysRevE.70.056114

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.

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