Instability, spinodal decomposition, and nucleation in a system with continuous symmetry

Abstract

The growth kinetics of the time-dependent Ginzburg-Landau model is studied in the large-N limit. Quenches from an initial equilibrium state at infinite temperature to a temperature corresponding to an unstable state beneath the coexistence curve are studied for both a conserved order parameter (COP) and for a nonconserved order parameter (NCOP). In both cases the system grows the order corresponding to the final equilibrium state by growing domains of the new phases. These domains are reflected through the existence of a peak in the structure factors which is evolving toward a Bragg peak as time increases. We find that these peaks satisfy a scaling relation similar to that for the related cases with a scalar order parameter. The characteristic lengths in these scaling laws satisfy a power-law behavior, L(t)∼$t^a$, where a=(1/2) for a NCOP and a=(1/4) for a COP. Riding on top of the developing long-range order are the Nambu-Goldstone modes which, we show, build smoothly into the $q^{\mathrm{-}2}$ behavior in the transverse correlation functions. The time evolution of the system after an isothermal field reversal is also studied. The increase in the time characterizing the reversal of the magnetization is found to be approximately inversely proportional to the magnitude of the field reversal. No limit of stability is found.