Critical droplets and metastability for a Glauber dynamics at very low temperatures
Critical droplets and metastability for a Glauber dynamics at very low temperatures
复制标题
极低温度下格劳伯动力学的临界液滴和亚稳定性
DOI：
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发表时间：
1991
期刊：
影响因子：
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通讯作者：
R. Schonmann
中科院分区：
文献类型：
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作者：
E. Jordão Neves;R. Schonmann
我们考虑了具有Glauber动力学的铁磁自旋系统在有限二维环面中的亚稳态行为，在温度趋于零的极限下，在正磁场下，在所谓的路径方法中。首先，我们考虑从自旋为+1的单个矩形液滴在自旋为-1的海洋中开始的演化。我们表明，小液滴很可能会消失，而大液滴很可能会增长，这两种情况之间的阈值被明确定义，仅取决于外部场。这个结果被用来证明，从所有自旋向下（-1）的组态开始，导致所有自旋向上（+1）的更稳定组态的演化模式随着温度的消失而接近亚稳态行为：系统在一段不可预测的时间内保持接近-1，直到最终形成一个精确大小的临界方形液滴，并使衰变成核为+1在相对较短的时间内的总衰减时间的渐近幅度示出有关的能量势垒的高度，预期从启发式和平均场亚稳性研究。
We consider the metastable behavior in the so-called pathwise approach of a ferromagnetic spin system with a Glauber dynamics in a finite two dimensional torus under a positive magnetic field in the limit as the temperature goes to zero. First we consider the evolution starting from a single rectangular droplet of spins +1 in a sea of spins −1. We show that small droplets are likely to disappear while large droplets are likely to grow; the threshold between the two cases being sharply defined and depending only on the external field. This result is used to prove that starting from the configuration with all spins down (−1) the pattern of evolution leading to the more stable configuration with all spins up (+1) approaches, as the temperature vanishes, a metastable behavior: the system stays close to −1 for an unpredictable time until a critical square droplet of a precise size is eventually formed and nucleates the decay to +1 in a relatively short time. The asymptotic magnitude of the total decay time is shown to be related to the height of an energy barrier, as expected from heuristic and mean field studies of metastability.