Random interface growth in a random environment: renormalization group analysis of a simple model (Q268957)

The authors study one problem that is a part of modelling growth processes in various physical systems. There are many microscopic models that allow a description of such phenomena but the growth processes share many important features with nearly equilibrium critical systems: self-similar behavior including power-law dependencies with some universal exponents. Usually, for the description of these universal properties of the growth processes, some certain and simplified models are used. The Kardar-Parisi-Zhang (KPZ) model is typically taken as the coarse-grained growth model. It is based on deterministic nonlinear differential equations with Gaussian random noise \(f\); this model is omnipresent in many different situations having its own generalizations and modifications. Usually \(f = f(x)\) is a Gaussian random noise with zero mean. There are also several other generalizations of this model leading to different solutions having applications in many systems, but this is not always satisfactory. In many real systems their behavior, near some critical points, is very sensitive to external disturbances, gravity, finite-size effects, the presence of impurities (sensitive to initial conditions) and also strongly dependent on deterministic and chaotic flows. This paper shows a study of the influence of random (turbulent) motion of a fluid containing dissolved particles on the IR (infrared) behavior of a randomly growing interface, paying special attention to the effects of compressibility. The paper consists of seven sections. In Section 2, there is a presentation of the field theory formulation of the full stochastic problem with the diagram technique. The next section shows ultraviolet (UV) divergences of the model and demonstrates its multiplicative renormalizability. Section 4 shows how the renormalization group (RG) equations and the equations of critical scaling can be obtained. Then we have a study of fixed points of the RG equations and possible scaling regimes. As a result, we have information that the purely ``kinematic'' regime (the KPZ nonlinearity) is irrelevant in the Wilson sense, and the purely KPZ fixed point (turbulent transfer is irrelevant), the RG equations have a completely nontrivial fixed point, where both the nonlinearity and the mixing are important. The paper is concluded in Section 7.