NUCLEATION AND GROWTH FOR THE ISING MODEL IN d DIMENSIONS AT VERY LOW TEMPERATURES

• 成果类型: Article
• 署名作者: Cerf, Raphael; Manzo, Francesco
• 署名单位: Universite Paris Saclay; Roma Tre University
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/12-AOP801
• 发表日期: 2013
• 页码: 3697-3785
• 关键词: small transition-probabilities; markov-chains; bootstrap percolation; glauber dynamics; general domain; exit problem; metastability; droplets; relaxation

摘要

This work extends to dimension d >= 3 the main result of Dehghanpour and Schonmann. We consider the stochastic Ising model on Z(d) evolving with the Metropolis dynamics under a fixed small positive magnetic field h starting from the minus phase. When the inverse temperature beta goes to infinity, the relaxation time of the system, defined as the time when the plus phase has invaded the origin, behaves like exp(beta k(d)). The value k(d) is equal to k(d) =1/d+1(Gamma(1) +...+ Gamma(d)), where Gamma(i) is the energy of the i-dimensional critical droplet of the Ising model at zero temperature and magnetic field h.