Nonlinear relaxation at first-order phase transitions: A Ginzburg-Landau theory including fluctuations

Kinetics of phase transitions are investigated in systems with nonconserved one-component order parameter (i.e., generalized time-dependent Ginzburg-Landau models ind dimensions). The correct static critical behavior as well as fluctuation effects on the kinetics are incorporated by a suitable adaptation of the theory on spinodal decomposition by Langer, Baron and Miller. Both the case of quenches from temperaturesT above to below the critical pointT _c and the case of magnetic field changesH from positive to negative values are treated, and both time-dependent order parameter m() and structure factorS(q, ) are obtained numerically ford=2, 3. In the case of quenches atH=0, we find that m()0 andS(q, ) —S(q, ) exp(– ^1/2/7.2) , withS(q, )q ^–2. In the case of field changes we find that forH not exceeding some critical valueH ^* the system is trapped in a metastable state with infinite lifetime. In contrast to the meanfield-spinodal, the susceptibility does not seem to diverge atH ^*. These results are compared with other treatments, in particular the Monte Carlo simulations of kinetic Ising models by Binder and Müller-Krumbhaar. While our theory describes some properties of the metastable states reasonably,H ^* distinctly exceeds the observed limit of metastability. We argue that the present theory does not take into account nucleation fluctuations, and also fails to describe correctly the domain growth in the late stages of the relaxation. Contrary to Langer et al. we suggest that universality holds for nonlinear relaxation and spinodal decomposition nearT _c .Supported in part by the Deutsche Forschungsgemeinschaft, Sonderforschungsbereich 130