Scaling and universality in coupled driven diffusive models

TL;DR

This paper investigates the universal scaling behavior of a coupled Burgers-like model inspired by 1d magnetohydrodynamics, revealing continuous variation of critical exponents with noise cross-correlation amplitude through analytical and numerical methods.

Contribution

It introduces a coupled Burgers-like model for 1d MHD and binary fluid mixtures, analyzing its universal properties and continuous dependence of scaling exponents on noise correlations.

Findings

Scaling exponents vary continuously with noise cross-correlation amplitude.

Numerical and analytical results are consistent and show long-wavelength physics dependence.

Lattice-gas models exhibit similar universal behavior.

Abstract

Inspired by the physics of magnetohydrodynamics (MHD) a simplified coupled Burgers-like model in one dimension (1d), a generalization of the Burgers model to coupled degrees of freedom, is proposed to describe 1dMHD. In addition to MHD, this model serves as a 1d reduced model for driven binary fluid mixtures. Here we have performed a comprehensive study of the universal properties of the generalized d-dimensional version of the reduced model. We employ both analytical and numerical approaches. In particular, we determine the scaling exponents and the amplitude-ratios of the relevant two-point time-dependent correlation functions in the model. We demonstrate that these quantities vary continuously with the amplitude of the noise cross-correlation. Further our numerical studies corroborate the continuous dependence of long wavelength and long time-scale physics of the model on the amplitude of the noise cross-correlations, as found in our analytical studies. We construct and simulate lattice-gas models of coupled degrees of freedom in 1d, belonging to the universality class of our coupled Burgers-like model, which display similar behavior. We use a variety of numerical (Monte-Carlo and Pseudospectral methods) and analytical (Dynamic Renormalization Group, Self-Consistent Mode-Coupling Theory and Functional Renormalization Group) approaches for our work. The results from our different approaches complement one another. Possible realizations of our results in various nonequilibrium models are discussed.