Renormalization group calculation of dynamic exponent in the models E and F with hydrodynamic fluctuations

TL;DR

This paper uses renormalization group techniques to analyze the dynamic critical behavior of models E and F with hydrodynamic fluctuations, providing one-loop results for the dynamic exponent and fixed-point stability.

Contribution

It introduces a renormalization group analysis of models E and F incorporating velocity fluctuations, with new calculations of the dynamic exponent in turbulent regimes.

Findings

Calculated the dynamic exponent z in turbulent regimes.

Analyzed the fixed-point structure and stability for model E.

Provided one-loop approximation results for anomalous dimensions.

Abstract

The renormalization group method is applied in order to analyze models E and F of critical dynamics in the presence of velocity fluctuations generated by the stochastic Navier-Stokes equation. Results are given to the one-loop approximation for the anomalous dimension $\gamma_\lambda$ and fixed-points' structure. The dynamic exponent $z$ is calculated in the turbulent regime and stability of the fixed points for the standard model E is discussed.