Bond percolation in frustrated systems

• 成果类型: Article
• 署名作者: De Santis, E; Gandolfi, A
• 署名单位: Sapienza University Rome; University of Rome Tor Vergata
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/aop/1022874815
• 发表日期: 1999
• 页码: 1781-1808
• 关键词: spin-glasses; BEHAVIOR; models; phase

摘要

We study occurrence and properties of percolation of occupied bonds in systems with random interactions and, hence, frustration. We develop a general argument, somewhat like Peierls' argument, by which we show that in Z(d), d greater than or equal to 2, percolation occurs for all possible interactions (provided they are bounded away from zero) if the parameter p is an element of (0, 1), regulating the density of occupied bonds, is high enough. If the interactions are i.i.d. random variables then we determine bounds on the values of p for which percolation occurs for all, almost all but not all, almost none but some, or none of the interactions. Motivations of this work come from the rigorous analysis of phase transitions in frustrated statistical mechanics systems.