A renormalization scheme and skewness of height fluctuations in (1  +  1)-dimensional VLDS dynamics

Singha, Tapas; Nandy, Malay K.

doi:10.1088/1742-5468/2016/02/023205

Cited by 9 publications

(13 citation statements)

References 46 publications

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“…II. Larger ratios (|S| ≈ 0.32 and |K| ≈ 0.1 in d = 1 + 1 and |S| ≈ 0.20 in d = 2 + 1) have also been reported for the steady state HDs of the CRSOS model [28], while a much smaller skewness (|S| ≈ 0.0441) was recently found in a (one-loop) renormalization anal- ysis of the nMBE equation in this regime [29].…”

mentioning

confidence: 56%

Universality and dependence on initial conditions in the class of the nonlinear molecular beam epitaxy equation

Carrasco

2016

Phys. Rev. E

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We report extensive numerical simulations of growth models belonging to the nonlinear molecular beam epitaxy (nMBE) class, on flat (fixed-size) and expanding substrates (ES). In both d=1+1 and 2+1, we find that growth regime height distributions (HDs), and spatial and temporal covariances are universal, but are dependent on the initial conditions, while the critical exponents are the same for flat and ES systems. Thus, the nMBE class does split into subclasses, as does the Kardar-Parisi-Zhang (KPZ) class. Applying the "KPZ ansatz" to nMBE models, we estimate the cumulants of the 1+1 HDs. Spatial covariance for the flat subclass is hallmarked by a minimum, which is not present in the ES one. Temporal correlations are shown to decay following well-known conjectures.

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mentioning

confidence: 56%

Universality and dependence on initial conditions in the class of the nonlinear molecular beam epitaxy equation

Carrasco

2016

Phys. Rev. E

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“…where k n = − n−1 j=1 k j , ω n = − n−1 j=1 ω j . The function L n is perturbatively computed to one loop order [43][44][45][46] as L n = (2D)δ n,2 + L n,1 ,…”

Section: Cumulantsmentioning

confidence: 99%

“…While λ and D do not renormalize and are thus scaleindependent, the coarse-grained linear coefficient ν(k) depends on wave vector as ν(k) ≃ (6Dλ 2 /π) 1/3 |k| −1 (see Appendix A 1 for details). We exploit this fact to estimate by DRG the cumulants of the statistical distribution of φ, following the methodology successfully employed for the KPZ [43][44][45] and NLMBE [46] equations. Thus, the n-th cumulant reads…”

Section: A Drg Evaluation Of Cumulantsmentioning

confidence: 99%

Gaussian statistics as an emergent symmetry of the stochastic scalar Burgers equation

Rodríguez-Fernández

Cuerno

2019

Phys. Rev. E

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Symmetries play a conspicuous role in the large-scale behavior of critical systems. In equilibrium they allow to classify asymptotics into different universality classes and, out of equilibrium, they sometimes emerge as collective properties which are not explicit in the "bare" interactions. Here we elucidate the emergence of an up-down symmetry in the asymptotic behavior of the stochastic scalar Burgers equation in one and two dimensions, manifested by the occurrence of Gaussian fluctuations even within the time regime controlled by nonlinearities. This robustness of Gaussian behavior contradicts naive expectations, due to the detailed relation -including the lack of up-down symmetry-between Burgers equation and the Kardar-Parisi-Zhang equation, which paradigmatically displays non-Gaussian fluctuations described by Tracy-Widom distributions. We reach our conclusions via a dynamic renormalization group study of the field statistics, confirmed by direct evaluation of the field probability distribution function from numerical simulations of the dynamical equation.

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“…This equation was independently proposed by Villain [4] and by Lai and Das Sarma [5] being also known as the Villain-Lai-Das Sarma (VLDS) equation and it is a standard model of the nonlinear molecular beam epitaxy (nMBE) universality class. This * eluis@ufba.br † thiagoaa@ufba.br ‡ silviojr@ufv.br equation has been investigated in the framework of renormalization group [6][7][8][9][10] and many features observed in kinetic Monte Carlo simulations have been elucidated. MBE is often modeled by microscopic transition rules built to capture the atomistic mechanisms.…”

Section: Introductionmentioning

confidence: 99%

Optimal detrended fluctuation analysis as a tool for the determination of the roughness exponent of the mounded surfaces

2017

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We present an optimal detrended fluctuation analysis (DFA) and applied it to evaluate the local roughness exponent in non-equilibrium surface growth models with mounded morphology. Our method consists in analyzing the height fluctuations computing the shortest distance of each point of the profile to a detrending curved that fits the surface within the investigated interval. We compare the optimal DFA (ODFA) with both the standard DFA and nondetrended analysis. We validate the ODFA method considering a one-dimensional model in the Kardar-Parisi-Zhang universality class starting from a mounded initial condition. We applied the methods to the Clarke-Vvdensky (CV) model in 2 + 1 dimensions with thermally activated surface diffusion and absence of step barriers. It is expected that this model belongs to the nonlinear Molecular Beam Epitaxy (nMBE) universality class. However, an explicit observation of the roughness exponent in agreement with the nMBE class was still missing. The effective roughness exponent obtained with ODFA agrees with the value expected for nMBE class whereas using the other methods it does not. We also characterized the transient anomalous scaling of the CV model and obtained that the corresponding exponent is in agreement with the value reported for other nMBE models with weaker corrections to the scaling.

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A renormalization scheme and skewness of height fluctuations in (1 + 1)-dimensional VLDS dynamics

Cited by 9 publications

References 46 publications

Universality and dependence on initial conditions in the class of the nonlinear molecular beam epitaxy equation

Universality and dependence on initial conditions in the class of the nonlinear molecular beam epitaxy equation

Gaussian statistics as an emergent symmetry of the stochastic scalar Burgers equation

Optimal detrended fluctuation analysis as a tool for the determination of the roughness exponent of the mounded surfaces

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