Scaling function ??0 asymptotics of the correlation function in theO n ?4 model

Antonov, N. V.; Васильев, А. Н.; Stepanenko, A. S.

doi:10.1007/bf01016349

Cited by 3 publications

(28 citation statements)

References 4 publications

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“…The precise form of the cutoff is unimportant; the sharp cutoff is the most convenient choice from the calculational viewpoint. We apply the standard field theoretic renormalization group (RG) to the modified model of erosion with turbulent mixing and arrive at the results similar to those presented in [26].…”

Section: Introduction and Description Of The Modelmentioning

confidence: 86%

“…In section 5 attractors of the obtained RG equations are analyzed in the infinitedimensional space of coupling constants. Instead of a set of fixed points (like for most multicoupling models), there are two two-dimensional surfaces of fixed points -one of them corresponds to IR asymptotic regime, where turbulent mixing is irrelevant, and coincides with the surface obtained in [26]. These surfaces are likely to contain IR attractive region(s).…”

Section: Introduction and Description Of The Modelmentioning

confidence: 89%

“…A model of landscape erosion of a surface with a fixed mean tilt was proposed in [14,15]. In [26] it was shown that the proposed model is only renormalizable if it is modified to include the whole series in the powers of h -the height of the propfileinstead of just its leading terms.…”

Section: Introduction and Description Of The Modelmentioning

confidence: 99%

“…The stochastic differential equation for the height of the profile, i.e. for the height field h(x) = h(t, x), proposed in [14,15] and modified in [26], is taken in the form…”

Section: Introduction and Description Of The Modelmentioning

confidence: 99%

“…In [14,15] is was taken odd in h which was explained by the symmetry h, f → −h, −f (another symmetry of the model is x → −x ). The authors of [14,15] also truncated the Taylor expansion of V (h) on the leading h 3 term, but the whole series in h should be considered instead [26].…”

Section: Introduction and Description Of The Modelmentioning

confidence: 99%

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Scaling in erosion of landscapes: renormalization group analysis of a model with turbulent mixing

Antonov¹,

Kakin²

2017

J. Phys. A: Math. Theor.

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Abstract. The model of landscape erosion, introduced in [Phys. Rev. Lett. 80: 4349 (1998); J. Stat. Phys. 93: 477 (1998)] and modified in [Theor. Math. Phys. -in press; arXiv:1602.00432], is advected by anisotropic velocity field. The field is Gaussian with vanishing correlation time and the pair correlation function of the form, where k ⊥ = |k ⊥ | and k ⊥ is the component of the wave vector, perpendicular to a certain preferred direction -the d-dimensional generalization of the ensemble introduced by Avellaneda and Majda [Commun. Math. Phys. 131: 381 (1990)]. Analogous to the case without advection, the model is multiplicatively renormalizable and has infinitely many coupling constants. The one-loop counterterm is derived in a closed form in terms of the certain function V (h), entering the original stochastic equation, and its derivatives with respect to the height field h(t, x). The full infinite set of the one-loop renormalization constants, β-functions and anomalous dimensions is obtained from the Taylor expansion of the counter-term. Instead of a two-dimensional surface of fixed points there is two such surfaces; they are likely to contain infrared attractive region(s). If that is the case, the model exhibits scaling behaviour in the infrared range. The corresponding critical exponents are nonuniversal because they depend on the coordinates of the fixed points on the surface; they also satisfy certain universal exact relation.

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Section: Introduction and Description Of The Modelmentioning

confidence: 86%

Section: Introduction and Description Of The Modelmentioning

confidence: 89%

Section: Introduction and Description Of The Modelmentioning

confidence: 99%

“…The stochastic differential equation for the height of the profile, i.e. for the height field h(x) = h(t, x), proposed in [14,15] and modified in [26], is taken in the form…”

Section: Introduction and Description Of The Modelmentioning

confidence: 99%

Section: Introduction and Description Of The Modelmentioning

confidence: 99%

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Scaling in erosion of landscapes: renormalization group analysis of a model with turbulent mixing

Antonov¹,

Kakin²

2017

J. Phys. A: Math. Theor.

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Anomalous scaling of passive scalar fields advected by the Navier-Stokes velocity ensemble: Effects of strong compressibility and large-scale anisotropy

Antonov

Kostenko

2014

Phys. Rev. E

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The field theoretic renormalization group and the operator product expansion are applied to two models of passive scalar quantities (the density and the tracer fields) advected by a random turbulent velocity field. The latter is governed by the Navier-Stokes equation for compressible fluid, subject to external random force with the covariance ∝δ(t-t')k(4-d-y), where d is the dimension of space and y is an arbitrary exponent. The original stochastic problems are reformulated as multiplicatively renormalizable field theoretic models; the corresponding renormalization group equations possess infrared attractive fixed points. It is shown that various correlation functions of the scalar field, its powers and gradients, demonstrate anomalous scaling behavior in the inertial-convective range already for small values of y. The corresponding anomalous exponents, identified with scaling (critical) dimensions of certain composite fields ("operators" in the quantum-field terminology), can be systematically calculated as series in y. The practical calculation is performed in the leading one-loop approximation, including exponents in anisotropic contributions. It should be emphasized that, in contrast to Gaussian ensembles with finite correlation time, the model and the perturbation theory presented here are manifestly Galilean covariant. The validity of the one-loop approximation and comparison with Gaussian models are briefly discussed.

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Fixed $d$ Renormalization Group Analysis of Conserved Surface Roughening

Skultety,

Honkonen

2021

Preprint

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Conserved surface roughening represents a special case of interface dynamics where the total height of the interface is conserved. Recently, it was suggested [F. Caballero et al., Phys. Rev. Lett. 121, 020601 (2018)] that the original continuum model known as 'Conserved Kardar-Parisi-Zhang'(CKPZ) equation is incomplete, as additional non-linearity is not forbidden by any symmetry in d > 1. In this work, we perform detailed field-theoretic renormalization group (RG) analysis of a general stochastic model describing conserved surface roughening. Systematic power counting reveals additional marginal interaction at the upper critical dimension, which appears also in the context of molecular beam epitaxy. Depending on the origin of the surface particle's mobility, the resulting model shows two different scaling regimes; If the particles move mainly due to the gravity, the leading dispersion law is ω ∼ k 2 , and the mean-field approximation describing a flat interface is exact in any spatial dimension. On the other hand, if the particles move mainly due to the surface curvature, the interface becomes rough with the mean-field dispersion law ω ∼ k 4 , and the corrections to scaling exponents must be taken into account. We show, that the latter model consist of two sub-class of models that are decoupled in all orders of perturbation theory. Moreover, our RG analysis of the general model reveals that the universal scaling is described by a rougher interface than CKPZ universality class. The universal exponents are derived within the one-loop approximation in both fixed d and ε-expansion schemes, and their relation is discussed. We point out all important details behind these two schemes which are often overlooked in the literature, and their misinterpretation might lead to inconsistent results.

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Scaling function ??0 asymptotics of the correlation function in theO n ?4 model

Cited by 3 publications

References 4 publications

Scaling in erosion of landscapes: renormalization group analysis of a model with turbulent mixing

Scaling in erosion of landscapes: renormalization group analysis of a model with turbulent mixing

Anomalous scaling of passive scalar fields advected by the Navier-Stokes velocity ensemble: Effects of strong compressibility and large-scale anisotropy

Fixed $d$ Renormalization Group Analysis of Conserved Surface Roughening

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