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The Percolation Signature of the Spin Glass Transition

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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 ±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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Authors and Affiliations

  1. Physics Department, University of Massachusetts, Amherst, MA, 01003, USA

    J. Machta

  2. Courant Institute of Mathematical Sciences, New York University, New York, NY, 10012, USA

    C. M. Newman

  3. Physics Department and Courant Institute of Mathematical Sciences, New York University, New York, NY, 10012, USA

    D. L. Stein

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  1. J. Machta
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  2. C. M. Newman
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  3. D. L. Stein
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Correspondence to J. Machta.

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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

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