Delayed Nucleation at a Weakly First-Order Transition

The dynamics of the transformation out of a nonequilibrium metastable phase is discussed within a mean-field theory at temperatures below the transition temperature $T_c$. We show that fluctuations are important and lead to an unusual time dependence of the order parameter, in particular a sharp delay time for the onset of the stable phase. This model is applied to the dynamics of the paraelectric to ferroelectric transition in BaTi${\mathrm{O}}_3$ where the mediating forces arise from long-range strain fields.