A Percolation-Theoretic Approach to Spin Glass Phase Transitions
Abstract
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 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.
Keywords
Cite
@article{arxiv.0805.0794,
title = {A Percolation-Theoretic Approach to Spin Glass Phase Transitions},
author = {J. Machta and C. M. Newman and D. L. Stein},
journal= {arXiv preprint arXiv:0805.0794},
year = {2008}
}
Comments
Based on lectures given at the 2007 Paris Summer School "Spin Glasses." 12 pages, 3 figures