Metastability in the dilute Ising model

• 成果类型: Article
• 署名作者: Bodineau, Thierry; Graham, Benjamin; Wouts, Marc
• 署名单位: Universite PSL; Ecole Normale Superieure (ENS); University of Warwick; Universite Paris 13
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-012-0474-8
• 发表日期: 2013
• 页码: 955-1009
• 关键词: equilibrium; relaxation; percolation; crystals

摘要

Consider Glauber dynamics for the Ising model on the hypercubic lattice with a positive magnetic field. Starting from the minus configuration, the system initially settles into a metastable state with negative magnetization. Slowly the system relaxes to a stable state with positive magnetization. Schonmann and Shlosman showed that in the two dimensional case the relaxation time is a simple function of the energy required to create a critical Wulff droplet. The dilute Ising model is obtained from the regular Ising model by deleting a fraction of the edges of the underlying graph. In this paper we show that even an arbitrarily small dilution can dramatically reduce the relaxation time. This is because of a catalytic effect-rare regions of high dilution speed up the transition from minus phase to plus phase.