Physica A 190 (1992) 145-160 North-Holland ~V~ICI l~ Dynamics of an Ising ferromagnet at T from the droplet model approach Vitaly A. Shneidman 1 Department of Materials Science and Engineering, The University of Arizona, Tucson, AZ 85721, USA Received 30 March 1992 Revised manuscript received 5 June 1992 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~ analytic and computer results correspond to each other with very few matching parameters, at T = T~ 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~ are also discussed. 1. Introduction In recent papers by Stauffer and Kert6sz [1] transient behavior of a 2D Ising ferromagnet driven by Glauber dynamics was studied using computer simula- tions. Unlike other studies of this kind which focused mainly on the autocorre- lation function (see, e.g., ref. [2]) the main concern of the mentioned papers was the cluster population time-dependence. It was also suggested to compare the simulation results with the solutions of the nucleation-type equation which describes the droplet model in the dynamic case. In the present study we are going to carry out this comparison and assess the applicability of the droplet model. For that purpose at T < T c we use and refine the asymptotic solution of the nucleation equation derived by the present author in ref. [3]. Alternatively, an exact solution is employed at T = T c where the asymptotic approach is inadequate. Present address: School of Theoretical Physics, The University of Augsburg, W-8900 Augs- burg, Germany. 0378-4371/92/$05.00 © 1992- Elsevier Science Publishers B.V. All rights reserved