Field Theoretic Renormalization Group in an Infinite-Dimensional Model of Random Surface Growth in Random Environment
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arXiv
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| Format: | Preprint |
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2024
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| author | Antonov, N. V. Babakin, A. A. Gulitskiy, N. M. Kakin, P. I. |
| author_facet | Antonov, N. V. Babakin, A. A. Gulitskiy, N. M. Kakin, P. I. |
| contents | The influence of a random environment on the dynamics of a fluctuating rough surface is investigated using a 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 fulfilling 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 problem allows for the large-scale, long-time scaling behaviour. For the first surface (advection is irrelevant) the critical dimensions of the height field $Δ_{h}$, the response field $Δ_{h'}$ and the frequency $Δ_ω$ are non-universal through the dependence on the effective couplings. For the other two surfaces (advection is relevant) the dimensions are universal and they are found exactly. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_13783 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Field Theoretic Renormalization Group in an Infinite-Dimensional Model of Random Surface Growth in Random Environment Antonov, N. V. Babakin, A. A. Gulitskiy, N. M. Kakin, P. I. Statistical Mechanics Chaotic Dynamics The influence of a random environment on the dynamics of a fluctuating rough surface is investigated using a 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 fulfilling 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 problem allows for the large-scale, long-time scaling behaviour. For the first surface (advection is irrelevant) the critical dimensions of the height field $Δ_{h}$, the response field $Δ_{h'}$ and the frequency $Δ_ω$ are non-universal through the dependence on the effective couplings. For the other two surfaces (advection is relevant) the dimensions are universal and they are found exactly. |
| title | Field Theoretic Renormalization Group in an Infinite-Dimensional Model of Random Surface Growth in Random Environment |
| topic | Statistical Mechanics Chaotic Dynamics |
| url | https://arxiv.org/abs/2407.13783 |