The Percolation Signature of the Spin Glass Transition
Abstract
Magnetic ordering at low temperature for Ising ferromagnets manifests itself within the associated Fortuin-Kasteleyn (FK) random cluster representation as the occurrence of a single positive density percolating network. In this paper we investigate the percolation signature for Ising spin glass ordering -- both in short-range (EA) and infinite-range (SK) models -- within a two-replica FK representation and also within the different Chayes-Machta-Redner two-replica graphical representation. Based on numerical studies of the EA model in three dimensions and on rigorous results for the SK model, we conclude that the spin glass transition corresponds to the appearance of {\it two} percolating clusters of {\it unequal} densities.
Cite
@article{arxiv.0707.0073,
title = {The Percolation Signature of the Spin Glass Transition},
author = {J. Machta and C. M. Newman and D. L. Stein},
journal= {arXiv preprint arXiv:0707.0073},
year = {2009}
}
Comments
13 pages, 6 figures