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 ±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 two percolating clusters of unequal densities.
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Machta, J., Newman, C.M. & Stein, D.L. The Percolation Signature of the Spin Glass Transition. J Stat Phys 130, 113–128 (2008). https://doi.org/10.1007/s10955-007-9446-2
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DOI: https://doi.org/10.1007/s10955-007-9446-2