A Percolation-Theoretic Approach to Spin Glass Phase Transitions

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The magnetically ordered, low temperature phase of Ising ferro- magnets 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 two-replica FK representation and also in the different Chayes-Machta-Redner two-replica graphical representation. Numerical studies of the $\pm J$ 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.
Based on lectures given at the 2007 Paris Summer School "Spin Glasses." 12 pages, 3 figures

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Statistical Mechanics, Disordered Systems and Neural Networks

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http://salesiana.dossiersoluciones.com/handle/123456789/160481

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0805.0794
 http://arxiv.org/abs/0805.0794

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arXiv