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October 1999 Bond Percolation in Frustrated Systems
E. De Santis, A. Gandolfi
Ann. Probab. 27(4): 1781-1808 (October 1999). DOI: 10.1214/aop/1022874815


We study occurrence and properties of percolation of occupied bonds in systems withrandom interactions and, hence, frustration.We develop a general argument, somewhat like Peierls’ argument, by which we show that in $\mathbb{Z},d\geq2$, percolation occurs for all possible interactions (provided they are bounded away from zero) if the parameter $p \in 1$, 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.


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E. De Santis. A. Gandolfi. "Bond Percolation in Frustrated Systems." Ann. Probab. 27 (4) 1781 - 1808, October 1999.


Published: October 1999
First available in Project Euclid: 31 May 2002

zbMATH: 0968.60092
MathSciNet: MR1742888
Digital Object Identifier: 10.1214/aop/1022874815

Primary: 60K35
Secondary: 82A25 , 82A57 , 82A68

Keywords: frustration , Peierls’ argument , percolation , Spin glasses

Rights: Copyright © 1999 Institute of Mathematical Statistics


Vol.27 • No. 4 • October 1999
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