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

IF 1.3 3区 物理与天体物理 Q3 PHYSICS, MATHEMATICAL
N. V. Antonov, A. A. Babakin, N. M. Gulitskiy, P. I. Kakin
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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’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 \(\Delta _{h}\), the response field \(\Delta _{h'}\) and the frequency \(\Delta _{\omega }\) 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.

Abstract Image

随机环境中随机表面生长的无限维模型中的场论重正化群
利用场理论重整化群研究了随机环境对波动粗糙表面动力学的影响。环境运动由随机Navier-Stokes方程模拟,该方程既包括热平衡流体,也包括湍流流体。该曲面由广义Pavlik随机方程描述。由于可重整性的要求,该模型必然涉及无限数量的耦合常数。单环反项以显式封闭形式导出。相应的重整化群方程证明了无限维参数空间中三个不动点二维曲面的存在性。如果表面包含红外吸引区域,则该模型允许大规模,长时间缩放行为。对于第一个表面(平流无关),高度场\(\Delta _{h}\)、响应场\(\Delta _{h'}\)和频率\(\Delta _{\omega }\)的临界尺寸由于依赖于有效耦合而非普适性。对于其他两个面(平流面是相关的),这些尺寸似乎是通用的,并且被精确地发现。
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来源期刊
Journal of Statistical Physics
Journal of Statistical Physics 物理-物理:数学物理
CiteScore
3.10
自引率
12.50%
发文量
152
审稿时长
3-6 weeks
期刊介绍: The Journal of Statistical Physics publishes original and invited review papers in all areas of statistical physics as well as in related fields concerned with collective phenomena in physical systems.
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