N. V. Antonov, A. A. Babakin, N. M. Gulitskiy, P. I. Kakin
{"title":"Field Theoretic Renormalization Group in an Infinite-Dimensional Model of Random Surface Growth in Random Environment","authors":"N. V. Antonov, A. A. Babakin, N. M. Gulitskiy, P. I. Kakin","doi":"10.1007/s10955-025-03410-3","DOIUrl":null,"url":null,"abstract":"<div><p>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 <span>\\(\\Delta _{h}\\)</span>, the response field <span>\\(\\Delta _{h'}\\)</span> and the frequency <span>\\(\\Delta _{\\omega }\\)</span> 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.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"192 2","pages":""},"PeriodicalIF":1.3000,"publicationDate":"2025-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Statistical Physics","FirstCategoryId":"101","ListUrlMain":"https://link.springer.com/article/10.1007/s10955-025-03410-3","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"PHYSICS, MATHEMATICAL","Score":null,"Total":0}
引用次数: 0
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.
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.