Kinetics of ordering in fluctuation-driven first-order transitions: simulation and theory

Abstract

Many systems involving competing interactions or interactions that compete with constraints are well described by a model first introduced by Brazovskii [Zh. Eksp. Teor. Fiz. 68, 175 (1975) [Sov. Phys. JETP 41, 85 (1975)]]. The hallmark of this model is that the fluctuation spectrum is isotropic and has a maximum at a nonzero wave vector represented by the surface of a d-dimensional hypersphere. It was shown by Brazovskii that the fluctuations change the free energy structure from a straight phi(4) to a straight phi(6) form with the disordered state metastable for all quench depths. The transition from the disordered phase to the periodic lamellar structure changes from second order to first order and suggests that the dynamics is governed by nucleation. Using numerical simulations we have confirmed that the equilibrium free energy function is indeed of a straight phi(6) form. A study of the dynamics, however, shows that, following a deep quench, the dynamics is described by unstable growth rather than nucleation. A dynamical calculation, based on a generalization of the Brazovskii calculations, shows that the disordered state can remain unstable for a long time following the quench.