Field Theoretic Renormalization Group in an Infinite-Dimensional Model of Random Surface Growth in Random Environment

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Field Theoretic Renormalization Group in an Infinite-Dimensional Model of Random Surface Growth in Random Environment. / Антонов, Николай Викторович ; Бабакин, Андрей Александрович ; Гулицкий, Николай Михайлович ; Какинь, Полина Игоревна.

в: Journal of Statistical Physics, Том 192, № 2, 33, 14.02.2025.

Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование

BibTeX

@article{49ba5a7ade1c408da4c09b5995722e29,

title = "Field Theoretic Renormalization Group in an Infinite-Dimensional Model of Random Surface Growth in Random Environment",

abstract = "The influence of a random environment on the dynamics of a fluctuating rough surface is investigated using the field theoretic renormalization group. The environment motion is modelled by the stochastic Navier–Stokes equation, which includes both a fluid in thermal equilibrium and a turbulent fluid. The surface is described by the generalized Pavlik{\textquoteright}s stochastic equation. As a result of the renormalizability requirement, the model necessarily involves an infinite number of coupling constants. The one-loop counterterm is derived in an explicit closed form. The corresponding renormalization group equations demonstrate the existence of three two-dimensional surfaces of fixed points in the infinite-dimensional parameter space. If the surfaces contain IR attractive regions, the model allows for a large-scale, long-time scaling behaviour. For the first surface (advection is irrelevant) the critical dimensions of the height field Δh, the response field Δh′ and the frequency Δω are non-universal through the dependence on the effective couplings. For the other two surfaces (advection is relevant) these dimensions appear to be universal and are found exactly.",

keywords = "Growth phenomena, Renormalizability, Renormalization group, Scaling behaviour",

author = "Антонов, {Николай Викторович} and Бабакин, {Андрей Александрович} and Гулицкий, {Николай Михайлович} and Какинь, {Полина Игоревна}",

year = "2025",

month = feb,

day = "14",

doi = "10.1007/s10955-025-03410-3",

language = "English",

volume = "192",

journal = "Journal of Statistical Physics",

issn = "0022-4715",

publisher = "Springer Nature",

number = "2",

}

RIS

TY - JOUR

T1 - Field Theoretic Renormalization Group in an Infinite-Dimensional Model of Random Surface Growth in Random Environment

AU - Антонов, Николай Викторович

AU - Бабакин, Андрей Александрович

AU - Гулицкий, Николай Михайлович

AU - Какинь, Полина Игоревна

PY - 2025/2/14

Y1 - 2025/2/14

N2 - The influence of a random environment on the dynamics of a fluctuating rough surface is investigated using the field theoretic renormalization group. The environment motion is modelled by the stochastic Navier–Stokes equation, which includes both a fluid in thermal equilibrium and a turbulent fluid. The surface is described by the generalized Pavlik’s stochastic equation. As a result of the renormalizability requirement, the model necessarily involves an infinite number of coupling constants. The one-loop counterterm is derived in an explicit closed form. The corresponding renormalization group equations demonstrate the existence of three two-dimensional surfaces of fixed points in the infinite-dimensional parameter space. If the surfaces contain IR attractive regions, the model allows for a large-scale, long-time scaling behaviour. For the first surface (advection is irrelevant) the critical dimensions of the height field Δh, the response field Δh′ and the frequency Δω are non-universal through the dependence on the effective couplings. For the other two surfaces (advection is relevant) these dimensions appear to be universal and are found exactly.

AB - The influence of a random environment on the dynamics of a fluctuating rough surface is investigated using the field theoretic renormalization group. The environment motion is modelled by the stochastic Navier–Stokes equation, which includes both a fluid in thermal equilibrium and a turbulent fluid. The surface is described by the generalized Pavlik’s stochastic equation. As a result of the renormalizability requirement, the model necessarily involves an infinite number of coupling constants. The one-loop counterterm is derived in an explicit closed form. The corresponding renormalization group equations demonstrate the existence of three two-dimensional surfaces of fixed points in the infinite-dimensional parameter space. If the surfaces contain IR attractive regions, the model allows for a large-scale, long-time scaling behaviour. For the first surface (advection is irrelevant) the critical dimensions of the height field Δh, the response field Δh′ and the frequency Δω are non-universal through the dependence on the effective couplings. For the other two surfaces (advection is relevant) these dimensions appear to be universal and are found exactly.

KW - Growth phenomena

KW - Renormalizability

KW - Renormalization group

KW - Scaling behaviour

UR - https://www.mendeley.com/catalogue/699fd711-3eb3-3413-8f01-d9d606d008bc/

U2 - 10.1007/s10955-025-03410-3

DO - 10.1007/s10955-025-03410-3

M3 - Article

VL - 192

JO - Journal of Statistical Physics

JF - Journal of Statistical Physics

SN - 0022-4715

IS - 2

M1 - 33

ER -

ID: 132274850