# The Percolation Signature of the Spin Glass Transition - Condensed Matter > Statistical Mechanics

Abstract: Magnetic ordering at low temperature for Ising ferromagnets manifests itselfwithin the associated Fortuin-Kasteleyn FK random cluster representation asthe occurrence of a single positive density percolating network. In this paperwe investigate the percolation signature for Ising spin glass ordering - bothin short-range EA and infinite-range SK models - within a two-replica FKrepresentation and also within the different Chayes-Machta-Redner two-replicagraphical representation. Based on numerical studies of the $\pm J$ EA model inthree dimensions and on rigorous results for the SK model, we conclude that thespin glass transition corresponds to the appearance of {\it two} percolatingclusters of {\it unequal} densities.

Author: J. Machta, C. M. Newman, D. L. Stein

Source: https://arxiv.org/