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

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 $N>1$.