A Percolation-Theoretic Approach to Spin Glass Phase Transitions

Simple item page
dc.creatorMachta, J.
dc.creatorNewman, C. M.
dc.creatorStein, D. L.
dc.date2008-05-06
dc.date.accessioned2026-07-07T09:37:31Z
dc.date.available2026-07-07T09:37:31Z
dc.descriptionThe 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.
dc.descriptionBased on lectures given at the 2007 Paris Summer School "Spin Glasses." 12 pages, 3 figures
dc.identifierhttps://arxiv.org/abs/0805.0794
dc.identifierhttp://arxiv.org/abs/0805.0794
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/160481
dc.subjectStatistical Mechanics
dc.subjectDisordered Systems and Neural Networks
dc.titleA Percolation-Theoretic Approach to Spin Glass Phase Transitions
dc.typetext

Files

Collections

arXiv