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The Metastable Behavior of the Three Dimensional Ising Model
The Metastable Behavior of the Three Dimensional Ising Model

陈大岳,冯建峰,钱敏平
Chen Dayue Feng Jianfeng Qian Minping

(Peking University, Beijing, 100871

收稿日期: 1993-04-25
出版日期: 1993-04-25

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摘要  The problem of metastability has attracted a great attention in the recent decade.In particular, it has been extensively investigated the 2-dimensional Ising model ina finite torus [CFQ]、[NS]、[Sch]. In this paper, the 3-dimensional Ising model withGlauber dynamics under a positive magnetic field is considered. We characterize themetastable behavior in the pathwise approacb, find out all metastable states, anddetermine naturally the critical droplet. We give a general and clear view of the sub-stance of the passage from all spins down (- 1) to all spins up (+ 1). For a largeclass of initial states, the logarithmic asymptotics of the hitting time of - 1 or + 1 areaccurately estimated, and the shrink and growth of droplets are described.
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