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 < Tc 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 = Tc 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 < Tc analytic and computer results correspond to each other with very few matching parameters, at T = Tc 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 Tc are also discussed.
|Original language||English (US)|
|Number of pages||16|
|Journal||Physica A: Statistical Mechanics and its Applications|
|State||Published - Nov 15 1992|
All Science Journal Classification (ASJC) codes
- Statistics and Probability
- Condensed Matter Physics