Erratum: Symmetry-based determination of space-time functions in nonequilibrium growth processes [Phys. Rev. E74, 061604 (2006)]

Abstract

The values of the nonuniversal constants 2 and D given in Table I of our paper are erroneous. Here we give the correct values of these quantities for the studied models ͑the Family model and the restricted Family model͒ in 1+1 and 2+1 dimensions ͓see Table I͔. Interestingly, the two models only differ through the value of the diffusion constant 2 . In Figs. 1-3 of our paper, we compared the numerically determined scaling function of the space-time correlation function with the exact solution Eq. ͑19͒ of the Edwards-Wilkinson equation. For this comparison, the values of 2 and D are plugged into the theoretical expression. Therefore, the erroneous values of the nonuniversal quantities also lead to erroneous theoretical curves that were used in the original figures. We show here the figures obtained with the correct values of 2 and D. We remark that the theoretical curves now perfectly describe the numerical data, even for small values of t / s for which some deviations were observed when using the erroneous values of 2 and D. The conclusion of our paper that both models belong to the universality class of the Edwards-Wilkinson equation not only remains unchanged, but it is now even much more convincing due to the perfect agreement between the numerical data and the exact solution of the stochastic Langevin equation. TABLE I. Estimates for the nonuniversal constants D and 2 . D 2 d = 1 6.26͑1͒ 0.794͑1͒ d = 1 restricted 6.27͑1͒ 0.770͑1͒ d = 2 38.9͑2͒ 0.686͑2͒ d = 2 restricted 38.5͑2͒ 0.372͑2͒ 0 1 0 2 0 r 2 /s 0.00 0.05 0.10 0.15 0.20 0.25 s -1/2 C(r 2 /s,t/s) s=100 s=50 s=25 Eq. (19) 0 2 0 4 0 t/s 0.00 0.05 0.10 0.15 0.20 s=100 s=25 Eq. (19) t/s=2 t/s=5 r 2 /s=1 r 2 /s=4FIG. 1. ͑Color online͒ Dynamical scaling of the space-time correlation function C͑r 2 / s , t / s͒ for the Family model in 1 + 1 dimensions with different values of the waiting time s: ͑a͒ C vs r 2 / s for some fixed values of t / s, ͑b͒ C vs t / s for some fixed values of r 2 / s. The green curves are obtained from the exact result ͓Eq. ͑19͔͒ derived from the continuum EW equations with uncorrelated Gaussian white noise. Numerical error bars are smaller than the sizes of the symbols.

Statistics of interfacial fluctuations of radially growing clusters

“…In more general terms, it is known that the different symmetries of statistical mechanical models influence their scaling properties [42,43]. It would be interesting to understand in complete generality the interplay among the symmetries of a physical model in a static domain and the asymmetric presence of dilution when we let this domain grow in time.…”

Relaxation dynamics of vortex lines in disordered type-II superconductors following magnetic field and temperature quenches

“…The dynamics of non-interacting directed lines in the absence of disorder can be directly mapped to the one-dimensional Edwards-Wilkinson interface growth model (which is in turn equivalent to a free noisy diffusion equation). The two-time height-height autocorrelation function (5) in the correlated regime is found to be [42] C(t, s) = C 0 s 1/2 t s + 1…”

“…In the free diffusive EdwardsWilkinson regime, the scaling exponent is b = 1/2 [32,42]. In our Langevin molecular dynamics study, we first analyze this case of free non-interacting vortex lines and start with the fixed magnetic field scenario to validate our numerical code.…”

Aging in coarsening diluted ferromagnets

“…It has been noted in the past 14,35 that space-and timedependent quantities are often better suited than quantities that only depend on time if one aims at studying the scaling properties of an aging system. Taking into account what we learned from the autocorrelation, namely, that the correct growth law L͑t͒ has to be used and that the observed simple scaling behavior means that the exponent B = 0, we should have that the autocorrelation function C͑t , s , r͒ is only a function of L͑t͒ / L͑s͒ and r / L͑t͒ ͓or, alternatively, of L͑t͒ / L͑s͒ and r / L͑s͔͒,…”

“…For systems undergoing phase ordering ͑as, for example, the perfect kinetic Ising model͒ it is usually found that b = 0, see Ref. 18 but some other classes of systems, for example, nonequilibrium growth systems, 35,36 are known to have b 0.…”