TY - JOUR

T1 - Renormalization group analysis of a continuous model with self-organized criticality: Effects of randomly moving environment

AU - Антонов, Николай Викторович

AU - Какинь, Полина Игоревна

AU - Лебедев, Никита Михайлович

AU - Лучин, Александр Юрьевич

PY - 2025/9

Y1 - 2025/9

N2 - 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 modelled 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.

AB - 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 modelled 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.

KW - Non-equilibrium critical behaviour

KW - Random environment

KW - Renormalization group

KW - Self-organized criticality

KW - Turbulence

UR - https://www.mendeley.com/catalogue/1c362a6f-5ed8-3a04-b311-81c1a35ab144/

U2 - 10.1016/j.nuclphysb.2025.117035

DO - 10.1016/j.nuclphysb.2025.117035

M3 - Article

VL - 1018

JO - Nuclear Physics B

JF - Nuclear Physics B

SN - 0550-3213

M1 - 117035

ER -