## 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 < 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.

Original language | English (US) |
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Pages (from-to) | 145-160 |

Number of pages | 16 |

Journal | Physica A: Statistical Mechanics and its Applications |

Volume | 190 |

Issue number | 1-2 |

DOIs | |

State | Published - Nov 15 1992 |

Externally published | Yes |

## All Science Journal Classification (ASJC) codes

- Statistics and Probability
- Condensed Matter Physics

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