Transport coefficients of O(N) scalar field theories close to the critical point

TL;DR

This paper studies the critical behavior of transport coefficients in O(N) scalar field theories near second-order phase transitions, revealing how shear and bulk viscosities behave differently depending on N.

Contribution

It formulates stochastic equations for slow modes and uses the dynamical renormalization group to analyze transport near criticality for arbitrary N.

Findings

Shear viscosity remains finite near the critical point.

Bulk viscosity diverges for N=1, but stays finite for N>1.

Model behavior transitions from model C to model G depending on N.

Abstract

We investigate the critical dynamics of O(N)-symmetric scalar field theories to determine the critical exponents of transport coefficients as a second-order phase transition is approached from the symmetric phase. A set of stochastic equations of motion for the slow modes is formulated, and the long wavelength dynamics is examined for an arbitrary number of field components, $N$, in the framework of the dynamical renormalization group within the $\epsilon$ expansion. We find that for a single component scalar field theory, N=1, the system reduces to the model C of critical dynamics, whereas for $N>1$ the model G is effectively restored owing to dominance of O(N)-symmetric charge fluctuations. In both cases, the shear viscosity remains finite in the critical region. On the other hand, we find that the bulk viscosity diverges as the correlation length squared, for N=1, while it remains finite for $N>1$.