Transport coefficients ofO(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 ε 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.

Bulk viscosity and the phase transition of the linear sigma model

“…In other words, the simplification of the large-N limit in some aspects of the model is also accompanied by an oversimplification of the dynamics that eventually gives rise to the absence of a maximum in the bulk viscosity. In fact, as we have already mentioned, from the dynamical renormalization group is not expected to have a divergence of the bulk viscosity in the large-N limit of this model [25]. This limit was also considered for the Gross-Neveu model in [24] and the results found there are perfectly compatible with ours.…”

“…However, a maximum of the bulk viscosity is not found in the large-N limit, consistent with other systems in the same limit as in [24]. Moreover, we find this result quite natural as recent dynamical renormalization group calculation shows that in this limit the bulk viscosity remains finite (it does not diverge) in the critical point [25].…”

“…However, this maximum at T c is not seen in other systems as in the Gross-Neveu model in the limit of a large number of fermion fields [24], where the bulk viscosity is a monotonically decreasing function when temperature increases. In the context of the O(N ) model it has been recently shown [25] that it belongs to model C if N = 1 and to model G if N > 1 (particularly the large-N limit) with a divergence with the correlation length if N = 1 going like ζ ∼ ξ 2 and being finite for N > 1 as ζ ∼ ξ 0 . In the hydrodynamic calculations of relativistic heavy-ion collisions, the bulk viscosity over entropy density can also be extracted.…”

Shear viscosity and phase diagram from Polyakov–Nambu–Jona-Lasinio model

“…It is seen that bulk viscosity and thermal conductivity strongly diverge and can be more important than shear viscosity near the QCD critical point. Another work using the same approach has been done in the framework of the O(N) scalar field theory [66] where the authors investigated the critical dynamics to determine the critical exponents of transport coefficients. The shear viscosity is found to remain finite for both single-and multicomponent theories in comparison to bulk viscosity which diverges for single-component theory.…”

Fluctuation sound absorption in quark matter

“…The idea goes back to the seminal paper [7] in which Mandelshtam and Leontovich formulated the slow relaxation time theory (see also [8][9][10][11][12]). Suppose that the relaxation time corresponding to the equilibrium restoration is large.…”