Kinetics of Ordering in Fluctuation-Driven First-Order Transitions: Simulations and Dynamical Renormalization

Details Kinetics of Ordering in Fluctuation-Driven First-Order Transitions: Simulations and Dynamical Renormalization Kinetics of Ordering in Fluctuation-Driven First-Order Transitions: Simulations and Dynamical Renormalization

2000-03-02

arxiv.org/abs/cond-mat/0003026v1

Physics

Condensed Matter

Soft Condensed Matter

18 pages, 15 figures submitted to PRE

Scientific paper

10.1103/PhysRevE.62.6116

Many systems where interactions compete with each other or with constraints are well described by a model first introduced by Brazovskii. Such systems include block copolymers, alloys with modulated phases, Rayleigh-Benard Cells and type-I superconductors. The hallmark of this model is that the fluctuation spectrum is isotropic and has a minimum at a nonzero wave vector represented by the surface of a d-dimensional hyper-sphere. It was shown by Brazovskii that the fluctuations change the free energy structure from a $ \phi ^{4}$ to a $\phi ^{6}$ form with the disordered state metastable for all quench depths. The transition from the disordered 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 $ \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.

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