Abstract
The metastable behavior of the stochastic Ising model is studied in a finite three-dimensional torus, in the limit as the temperature goes to zero. The so-called critical droplet is determined, a clear view of the passage from the configuration that all spins are down (-1) to the configuration that all spins axe up (+1) is given and the logarithmic asymptotics of the hitting time of+1 starting at -1 orvice versa is calculated. The proof uses large deviation estimates of a family of exponentially perturbed Markov chains.
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Chen, D., Feng, J., Qian, M. P., The metastable behavior of the three-dimensional stochastic Ising model (I),Science in China, Ser. A, 1997, 40(8): 832.
Chen, D., Feng, J., Qian, M. P., The metastability of exponentially perturbed Markov chains,Science in China, Ser. A, 1996, 39(1): 7.
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Project supported in part by a Postdoctoral Fellowship from the State Education Commission of China, and by the National Natural Science Foundation of China, the Tianyuan Foundation and the National 863 Project.
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Chen, D., Feng, J. & Qian, M. The metastable behavior of the three-dimensional stochastic Ising model (II). Sci. China Ser. A-Math. 40, 1129–1135 (1997). https://doi.org/10.1007/BF02931831
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DOI: https://doi.org/10.1007/BF02931831