Dynamics of an Ising ferromagnet at T≤ T_c from the droplet model approach

We consider a Fokker-Planck type kinetic equation for the cluster distribution, similar to the one used in nucleation theory. From the asymptotic solution of this equation at T < T_c we show that transition to equilibrium takes place through propagation of a "shock-wave" in the space of cluster sizes. This leads to a stretched-exponential magnetization time-dependence. At T = T_c an exact solution to the kinetic equation is derived. The results are compared to simulation data by Stauffer and Kertesz for cluster population in a 2D Ising ferromagnet driven by Glauber dynamics. While for T < T_c analytic and computer results correspond to each other with very few matching parameters, at T = T_c a strong deviation is observed which could mean the necessity of generalization of the kinetic equation. Inherent limitations of the droplet model which may be important even below T_c are also discussed.