Critical dynamics of Model H within the real-time fRG approach

TL;DR

This paper investigates the critical dynamics of Model H using the real-time functional renormalization group approach, deriving flow equations, fixed points, and critical exponents relevant to phase transitions in fluid systems.

Contribution

It introduces a real-time fRG framework for Model H, deriving flow equations and calculating critical exponents and transport coefficients with higher-order corrections.

Findings

Flow equations for Model H are derived.

Critical exponents and transport coefficients are estimated.

Dynamic critical exponent z is obtained as a function of dimension d.

Abstract

The critical dynamics of Model H with a conserved order parameter coupled to a transverse momentum density which describes the gas-liquid or binary-fluid transitions is investigated within the functional renormalization group approach formulated on the closed time path. According to the dynamic scaling analysis, Model H and QCD critical end point belong to the same dynamic universality class in the critical region. The higher-order correction of the transport coefficient $\bar\lambda$ and shear viscosity $\bar\eta$ arising from mode-couplings are obtained by calculating the two-point correlation functions. The flow equation of a dimensionless coupling constant for nondissipative interactions is derived to look for the fixed-point solution of the system. The scaling relation between the critical exponent of the transport coefficient and that of the shear viscosity is estimated. Finally, the dynamic critical exponent $z$ is obtained as a function of the spatial dimension $d$.