Critical behavior of certain non-equilibrium systems with a quenched random noise

Abstract

Four models of critical behavior with quenched noise are studied by the means of renormalization group analysis. The models include the Kardar—Parisi—Zhang model of an interface random growth and its modification with an infinite number of coupling constants, the Hwa—Kardar model of a system in a self-organized critical state, and the model of landscape erosion with an infinite number of coupling constants. The quenched noise is described by the correlation function ff ∝ δ(ω)/k4 (here k is a wave vector and ω is a frequency) and models variability of the studied profiles (e. g. growing interface, eroded landscape, etc.). For two models containing infinitely many coupling constants their critical exponents (that describe asymptotic — critical — behavior in an infrared range) satisfy a universal exact relation. For the models of the Kardar—Parisi— Zhang and Hwa—Kardar corresponding critical exponents are calculated to the first order of the expansion in the deviation from the logarithmic dimension (one-loop approximation). Refs 37. Tables 4.