Critical dynamics of a stochastic n-vector model below Tc

The dynamic properties of a stochastic n-vector model are investigated for T < Tc in d=4−ϵ dimensions. Besides the non-conserved order parameter the model involves also the conserved densities of generators of the symmetry group O(n). We calculate the excitation spectra of those conserved densities and the transverse fluctuations of the order parameter to linear order in ϵ in the hydrodynamic region kξ⪡1. The propagating modes have linear dispersion and quadratic damping in accordance with the phenomenological theory. The relaxing modes, however, exhibit non-hydrodynamic wavenumber dependence with a relaxation rate ωk ∞ kd2.