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Register a new userComment on cond-mat/0107371: ``Dynamical exponents of an even-parity-conserving contact process with diffusion
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Added by
Marcio Argollo de Menezes
Publication date
2001
fields
Physics
and research's language is
English
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In cond-mat/0107371, Mendonca proposes that diffusion can change the universality class of a parity-conserving reaction-diffusion process. In this comment we suggest that this cannot happen, due to symmetry arguments. We also present numerical results from lattice simulations which support these arguments, and mention a previous result supporting this conclusion.
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We study the pair contact process with diffusion (PCPD) using Monte Carlo simulations, and concentrate on the decay of the particle density $rho$ with time, near its critical point, which is assumed to follow $rho(t) approx ct^{-delta} +c_2t^{-delta_2}+...$. This model is known for its slow convergence to the asymptotic critical behavior; we therefore pay particular attention to finite-time corrections. We find that at the critical point, the ratio of $rho$ and the pair density $rho_p$ converges to a constant, indicating that both densities decay with the same powerlaw. We show that under the assumption $delta_2 approx 2 delta$, two of the critical exponents of the PCPD model are $delta = 0.165(10)$ and $beta = 0.31(4)$, consistent with those of the directed percolation (DP) model.
The pair contact process (PCP) is a nonequilibrium stochastic model which, like the basic contact process (CP), exhibits a phase transition to an absorbing state. The two models belong to the directed percolation (DP) universality class, despite the fact that the PCP possesses infinitely many absorbing configurations whereas the CP has but one. The critical behavior of the PCP with hopping by particles (PCPD) is as yet unclear. Here we study a version of the PCP in which nearest-neighbor particle {it pairs} can hop but individual particles cannot. Using quasistationary simulations for three values of the diffusion probability ($D=0.1$, 0.5 and 0.9), we find convincing evidence of DP-like critical behavior.
The pair contact process with diffusion (PCPD) is studied with a standard Monte Carlo approach and with simulations at fixed densities. A standard analysis of the simulation results, based on the particle densities or on the pair densities, yields inconsistent estimates for the critical exponents. However, if a well-chosen linear combination of the particle and pair densities is used, leading corrections can be suppressed, and consistent estimates for the independent critical exponents delta=0.16(2), beta=0.28(2) and z=1.58 are obtained. Since these estimates are also consistent with their values in directed percolation (DP), we conclude that PCPD falls in the same universality class as DP.
A recent e-print (cond-mat/0604532) presented a proposed Comment to Applied Physics Letters on our publication Appl. Phys. Lett. 88, 162503 (2006), cond-mat/0603260. Here is our Response. As the proposed Comment has now been rejected by Applied Physics Letters, neither the Comment nor the Response will be published in Applied Physics Letters in this form.
We investigate the influence of time-varying environmental noise, i.e., temporal disorder, on the nonequilibrium phase transition of the contact process. Combining a real-time renormalization group, scaling theory, and large scale Monte-Carlo simulations in one and two dimensions, we show that the temporal disorder gives rise to an exotic critical point. At criticality, the effective noise amplitude diverges with increasing time scale, and the probability distribution of the density becomes infinitely broad, even on a logarithmic scale. Moreover, the average density and survival probability decay only logarithmically with time. This infinite-noise critical behavior can be understood as the temporal counterpart of infinite-randomness critical behavior in spatially disordered systems, but with exchanged roles of space and time. We also analyze the generality of our results, and we discuss potential experiments.
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