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

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 $\epsilon$ and $\delta$ to calculate renormalization constants. Here, $\epsilon$ 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.

The authors thank the Organizers of the conference "Models in Quantum Field Theory IV, MQFT-2012" for the opportunity to present the results of the research summarised in the paper, 13 pages, 5 Tables

References in corpus (1)

• Effects of mixing and stirring on the critical behavior

Cited by in corpus (3)

• Superfluid Phase Transition with Activated Velocity Fluctuations: Renormalization Group Approach
• Renormalization group study of superfluid phase transition: effect of compressibility
• Renormalization group calculation of dynamic exponent in the models E and F with hydrodynamic fluctuations