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- Publisher
- Birkhäuser Basel
- Copyright
- © Birkhäuser Basel 2009
- ISBN
- 978-3-7643-8999-4
- Pages
- 205 –223
- DOI
- 10.1007/978-3-7643-9891-0_9
- Publisher site
- See Chapter on Publisher Site
Abstract
[The magnetically ordered, low temperature phase of Ising ferromagnets is manifested within the associated Fortuin—Kasteleyn (FK) random cluster representation by the occurrence of a single positive density percolating cluster. In this paper, we review our recent work on the percolation signature for Ising spin glass ordering — both in the short-range Edwards—Anderson (EA) and infinite-range Sherrington—Kirkpatrick (SK) models — within a tworeplica FK representation and also in the different Chayes—Machta—Redner two-replica graphical representation. Numerical studies of the ±J EA model in dimension three and rigorous results for the SK model are consistent in supporting the conclusion that the signature of spin-glass order in these models is the existence of a single percolating cluster of maximal density normally coexisting with a second percolating cluster of lower density.]
Published: Dec 14, 2009
Keywords: 82B44; 82D30; 82B80; 60K35; 82B43; 05C80; Ising spin glass; percolation; graphical representations; cluster algorithms; Fortuin—Kasteleyn