Condensation vs phase ordering in the dynamics of first-order transitions

The origin of the noncommutativity of the limits t-->infinity and N-->infinity in the dynamics of first-order transitions is investigated. In the large-N model, i.e., N-->infinity taken first, the low-temperature phase is characterized by condensation of the large-wavelength fluctuations rather than by genuine phase ordering as when t-->infinity is taken first. A detailed study of the scaling properties of the structure factor in the large-N model is carried out for quenches above, at, and below T-c. Preasymptotic scaling is found and crossover phenomena are related to the existence of components in the order parameter with different scaling properties. Implications for phase ordering in realistic systems are discussed.