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

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 $N>1$.

revised for publication in PRD

References in corpus (21)

• Viscosity Information from Relativistic Nuclear Collisions: How Perfect is the Fluid Observed at RHIC?
• A calculation of the bulk viscosity in SU(3) gluodynamics
• Influence of the shear viscosity of the quark-gluon plasma on elliptic flow in ultrarelativistic heavy-ion collisions
• Bulk viscosity of QCD matter near the critical temperature
• Dynamic universality class of the QCD critical point
• Perturbative QCD Calculations of Elliptic Flow and Shear Viscosity in Au+Au Collisions at $\sqrt{s_{NN}}=200$ GeV
• Second order hydrodynamic coefficients from kinetic theory
• Bulk viscosity in quasi particle models
• Shear and bulk viscosities of the gluon plasma in a quasiparticle description
• Shear Viscosity to Entropy Density Ratio of QCD below the Deconfinement Temperature
• QCD Viscosity to Entropy Density Ratio in the Hadronic Phase
• Non-perturbative Approach to Critical Dynamics
• Dynamic critical phenomena in the AdS/CFT duality
• Correlation functions of the energy-momentum tensor in SU(2) gauge theory at finite temperature
• Phase Transitions and the Perfectness of Fluids
• Critical phenomena in N=4 SYM plasma
• $\eta /s$ and Phase Transitions
• Renormalized Linear Kinetic Theory as Derived from Quantum Field Theory - a novel diagrammatic method for computing transport coefficients -
• Dynamic universality class of large-N gauge theories
• Dynamics near QCD critical point by dynamic renormalization group
• Shear Viscosity in Weakly Coupled N-Component Scalar Field Theories

Cited by in corpus (9)

• Bulk viscosity and the phase transition of the linear sigma model
• From quantum to classical dynamics: The relativistic $O(N)$ model in the framework of the real-time functional renormalization group
• Shear Viscosity and Phase Diagram from Polyakov$-$Nambu$-$Jona-Lasinio model
• Dynamics of non-Gaussian fluctuations in model A
• Many-body chaos near a thermal phase transition
• Fluctuation sound absorption in quark matter
• Many-body chaos and anomalous diffusion across thermal phase transitions in two dimensions
• Microscopic identification of dissipative modes in relativistic field theories
• Soft pions and transport near the chiral critical point