The Percolation Signature of the Spin Glass Transition

J. Machta; C. M. Newman; D. L. Stein

doi:10.1007/s10955-007-9446-2

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arXiv · 0707.0073

The Percolation Signature of the Spin Glass Transition

J. Machta·C. M. Newman·D. L. Stein

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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 $\pm J$ 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.

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J. Machta, C. M. Newman, D. L. Stein. 2007-06-30. The Percolation Signature of the Spin Glass Transition. https://doi.org/10.1007/s10955-007-9446-2

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