Influence of Hydrodynamic Fluctuations on the Phase Transition in Models E and F of Critical Dynamics

TL;DR

This paper investigates how velocity fluctuations influence the critical dynamics of models E and F using renormalization group techniques, revealing their impact on phase transition behavior.

Contribution

It introduces a field-theoretical model incorporating stochastic Navier-Stokes velocity fluctuations for model E, enabling perturbative renormalization group analysis and fixed-point study.

Findings

Model is multiplicatively renormalizable.

One-loop approximation results obtained.

Analysis of fixed-point structure provided.

Abstract

We use the renormalization group method to study model E of critical dynamics in the presence of velocity fluctuations arising in accordance with the stochastic Navier-Stokes equation. Using Martin-Siggia-Rose theorem, we obtain a field- theoretical model that allows a perturbative renormalization group analysis. By direct power counting and an analysis of ultraviolet divergences, we show that the model is multiplicatively renormalizable, and we use a two-parameter expansion in $\varepsilon$ and $\delta$ to calculate renormalization constants. Here, $\varepsilon$ is a deviation from the critical dimension four, and $\delta$ is a deviation from the Kolmogorov regime. We present the results of the one-loop approximation and part of the fixed-point structure. We briefly discuss the possible effect of velocity fluctuations on the large-scale behavior of the model.