Dynamics of an Ising ferromagnet at T⩽ Tc from the droplet model approach

Vitaly A. Shneidman

Physica A: Statistical Mechanics and its Applications, 1992, vol. 190, issue 1, 145-160

Abstract: 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.

Date: 1992
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:190:y:1992:i:1:p:145-160

DOI: 10.1016/0378-4371(92)90083-3

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