Temperature Dependence of Domain Kinetics in Two Dimensions

Monte Carlo simulations have been carried out to study the effect of temperature on the growth kinetics of a circular grain. As predicted by $d=3\mathrm{}$ theories of domain kinetics, the circular domain shrinks linearly with time as $A\left(t\right)=A_0-\alpha t$, where $A_0$ and $A\left(t\right)\mathrm{}$ are the initial and instantaneous areas, respectively. However, in contrast to $d=3\mathrm{}$, the slope $\alpha$ is strongly temperature dependent for $T>~0.6T_c$. An analytical theory which considers the thermal fluctuations agrees with the $T$ dependence of the Monte Carlo data in this regime.