The growth of order in a system with continuous symmetry is studied in the time-dependent Ginzburg-Landau model (in the large-N limit), quenched below the coexistence curve. The dynamics are studied with and without conservation of the order parameter. The development of order in the longitudinal direction and the buildup of Nambu-Goldstone modes in the transverse directions are explicitly exhibited. Nontrivial scaling behavior and growth laws are obtained in the long-time regime.
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Mazenko et al. (1984) studied this question.