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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| Online Access: | https://arxiv.org/abs/2505.13040 |
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| _version_ | 1866913958044106752 |
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| author | Antonov, N. V. Kakin, P. I. Lebedev, N. M. Luchin, A. Yu. |
| author_facet | Antonov, N. V. Kakin, P. I. Lebedev, N. M. Luchin, A. Yu. |
| contents | We study a strongly anisotropic self-organized critical system coupled to an isotropic random fluid environment. The former is described by a continuous (coarse-grained) model due to Hwa and Kardar. The latter is modeled by the Navier--Stokes equation with a random stirring force of a rather general form that includes, in particular, the overall shaking of the system and a non-local part with power-law spectrum $\sim k^{4-d-y}$ that describes, in the limiting case $y \to 4$, a turbulent fluid. The full problem of the two coupled stochastic equations is represented as a field theoretic model which is shown to be multiplicatively renormalizable and logarithmic at $d=4$. Due to the interplay between isotropic and anisotropic interactions, the corresponding renormalization group (RG) equations reveal a rich pattern of possible infrared (large scales, long times) regimes of asymptotic behaviour of various Green's functions. The attractors of the RG equations in the five-dimensional space of coupling parameters include a two-dimensional surface of Gaussian (free) fixed points, a single fixed point that corresponds to the plain advection by the turbulent fluid (the Hwa--Kardar self-interaction is irrelevant) and a one-dimensional curve of fixed points that corresponds to the case where the Hwa--Kardar nonlinearity and the uniform stirring are simultaneously relevant. The character of attractiveness is determined by the exponent $y$ and the dimension of space $d$; the most interesting case $d=3$ and $y \to 4$ is described by the single fixed point. The corresponding critical dimensions of the frequency and the basic fields are found exactly. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_13040 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Renormalization group analysis of a continuous model with self-organized criticality: Effects of randomly moving environment Antonov, N. V. Kakin, P. I. Lebedev, N. M. Luchin, A. Yu. Statistical Mechanics We study a strongly anisotropic self-organized critical system coupled to an isotropic random fluid environment. The former is described by a continuous (coarse-grained) model due to Hwa and Kardar. The latter is modeled by the Navier--Stokes equation with a random stirring force of a rather general form that includes, in particular, the overall shaking of the system and a non-local part with power-law spectrum $\sim k^{4-d-y}$ that describes, in the limiting case $y \to 4$, a turbulent fluid. The full problem of the two coupled stochastic equations is represented as a field theoretic model which is shown to be multiplicatively renormalizable and logarithmic at $d=4$. Due to the interplay between isotropic and anisotropic interactions, the corresponding renormalization group (RG) equations reveal a rich pattern of possible infrared (large scales, long times) regimes of asymptotic behaviour of various Green's functions. The attractors of the RG equations in the five-dimensional space of coupling parameters include a two-dimensional surface of Gaussian (free) fixed points, a single fixed point that corresponds to the plain advection by the turbulent fluid (the Hwa--Kardar self-interaction is irrelevant) and a one-dimensional curve of fixed points that corresponds to the case where the Hwa--Kardar nonlinearity and the uniform stirring are simultaneously relevant. The character of attractiveness is determined by the exponent $y$ and the dimension of space $d$; the most interesting case $d=3$ and $y \to 4$ is described by the single fixed point. The corresponding critical dimensions of the frequency and the basic fields are found exactly. |
| title | Renormalization group analysis of a continuous model with self-organized criticality: Effects of randomly moving environment |
| topic | Statistical Mechanics |
| url | https://arxiv.org/abs/2505.13040 |