TY - JOUR

T1 - Dynamics of an Ising ferromagnet at T≤ Tc from the droplet model approach

AU - Shneidman, Vitaly A.

N1 - Funding Information:
I wish to express my gratitude to D. Stauffer, who introduced me to the problems of transient dynamics of an Ising ferromagnet and suggested the present study. Also, I am very grateful to M.C. Weinberg for valuable discussions on the relation between asymptotic and exact solutions of the nucleation equation. This work was supported financially by the Jet Propulsion Laboratory and The Division of Microgravity Science and Applications of NASA.

PY - 1992/11/15

Y1 - 1992/11/15

N2 - 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.

AB - 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.

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U2 - 10.1016/0378-4371(92)90083-3

DO - 10.1016/0378-4371(92)90083-3

M3 - Article

AN - SCOPUS:26144431746

VL - 190

SP - 145

EP - 160

JO - Physica A: Statistical Mechanics and its Applications

JF - Physica A: Statistical Mechanics and its Applications

SN - 0378-4371

IS - 1-2

ER -