Kinetics of first-order phase transitions: Monte Carlo simulations, renormalization-group methods, and scaling for critical quenches

Using a combination of renormalization-group (RG) methods and Monte Carlo simulations, we study the growth kinetics of the spin-flip (SFKI) and the spin-exchange (SEKI) kinetic Ising models subjected to a critical quench (in zero external field) from infinite to low temperatures. The method developed here allows one to establish, in a nonperturbative fashion, the RG equations developed by us elsewhere. In the case of the SFKI model we find agreement, as expected, with the curvature-driven dynamics of Lifshitz, Cahn, and Allen which gives a growth law for a typical domain size of L(t)∼$t^{1/2}$. Our results for the SEKI model (spinodal decomposition) are qualitatively different from the SFKI case. While both show scaling behavior for quenches to nonzero temperatures, the growth kinetics for the SE case show a long-time logarithmic growth L(t)∼lnt. For intermediate times one can fit an effective exponent L(t)∼$t^{a\left(t\right)}$ where a(t) agrees well with existing direct Monte Carlo studies. This logarithmic behavior is associated with the freezing of this system for quenches to zero temperature.