Reply to “Comment on ‘Critical behavior of a two-species reaction-diffusion problem’ ”

Abstract

Recent Monte Carlo results ͓Phys. Rev. E 61, 6330 ͑2000͔͒ on the one-dimensional reaction-diffusion process AϩB→2B and B→A lead us to estimate ϭ2.21Ϯ0.05 for the correlation length exponent. The preceding Comment ͓Phys. Rev. E 64, 058101 ͑2001͔͒ advocates the exact value ϭ2. We show that Janssen's arguments leave enough doubts to justify an independent Monte Carlo determination of .In our work ͓1͔ referred to by the preceding Comment ͓2͔, we treated the exponent as an unknown, with the result ϭ2.21Ϯ0.05; any other value of deteriorates the fit to the order parameter curve, based on our Fig. 3 and the discussion of Sec. III A 2. We should have mentioned the relation ϭ2/d due to Kree, Schaub, and Schmittmann ͑KSS͒ ͓3͔, and commented on it not being satisfied in our dϭ1 simulation.Now the Comment asserts ͑although with a proviso: ''as long as one assumes . . . ''͒ that ϭ2 has to be inserted in the analysis of dϭ1 Monte Carlo data as if it were an established fact. ͓Anyone convinced of that only has to solve our equation ␤/ϭ0.197Ϯ0.002 ͓1͔ with ϭ2 ͑instead of ϭ2.21Ϯ0.05) to find ␤ϭ0.394Ϯ0.004 ͑instead of ␤ ϭ0.435Ϯ0.010); thereby sacrificing the fit to the orderparameter curve. ͔ We show below that the Comment is misguided in attempting to impose ϭ2 as an a priori truth, not in need of independent verification. The author's criticism of our exponent values on this basis is therefore inadmissible.Our value of was stated ͓1͔ not to take into account any possible systematic corrections. One is free to hope that if and when such corrections can be handled, they will reduce the Monte Carlo value of to 2. Alternatively, this may be a case where Janssen's arguments ͓2͔ do not apply and where 2.A good reason for their potential failure, and hence for circumspection, is of a well-known kind. The relation ϭ2/d depends on the existence of a fixed point having all the symmetries listed in the Comment. The existence of such a fixed point was demonstrated in an ⑀ expansion ͑the ''KSS fixed point'' ͓3͔͒, but is increasingly subject to doubt as d is lowered: The quartic terms in the action ͑see ͓4͔͒, which are irrelevant in the ⑀ expansion, may become relevant for d as far down as dϭ1. A warning signal ͑not a proof͒ is that at the Gaussian fixed point these terms are ''naively relevant'' for dϽ2, and that at the KSS fixed point, due to being negative, their scaling dimensions increase with ⑀.If the quartic terms are relevant in dϭ1, then, because they break the continuous symmetry on which ϭ2 is based, these terms destroy this relation. The discrete symmetries ͑IV and V in the Comment's notation͒, however, continue to be respected by the quartic terms ͓4͔, and it is hard to see how, even if they are relevant, these terms could affect the exponent relations that we used later on in our work ͓1͔. In particular, ϭ is guaranteed by the time-reversal symmetry of the action ͓4͔, quartic terms included. KSS define their model originally as a system of two coupled Langevin equations ͓ ͓3͔, Eqs. ͑2.1b͒ and ͑2.4͒-͑2.6͔͒, which leave the quar...

Integration of Langevin Equations with Multiplicative Noise and the Viability of Field Theories for Absorbing Phase Transitions

“…Performing with our scheme critical decay experiments in spatial dimensions d = 1, 2 we find the exponent θ to be undistinguishable from the DP values. Because this differs from both analytical predictions [18,19,23] and estimates from microscopic models [24], this indicates that the truncation of the full action of the field theory needed to arrive at the corresponding Langevin equations is not legitimate. The voter critical point.…”

“…Our results are particularly worthy in the context of the current debate about APTs occurring when ρ is coupled to an auxiliary field ψ: when ψ is static and conserved (Manna sandpile model, conserved-DP, or fixed energy sandpiles class) [9,13,14,15,16,17] we obtain the best numerical estimates for the critical indices. When ψ is conserved but diffuses [18,19,20,21,22,23,24], our results suggest that, at least in low spatial dimensions, the Langevin equations postulated or derived (approximately) as candidate field theories are not viable.…”

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Infinitely-many absorbing-state nonequilibrium phase transitions

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