2025/05/19 by Antonov, N. V., Kakin, P. I., Lebedev, N. M. +1
#FOS: Physical sciences #Statistical Mechanics (cond-mat.stat-mech)
paper · doi:10.48550/arxiv.2505.13040
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 ∼ k4-d-y that describes, in the limiting case y → 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 → 4 is described by the single fixed point. The corresponding critical dimensions of the frequency and the basic fields are found exactly.