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Unpublished Paper
Percolation in the Sherrington-Kirkpatrick Spin Glass
Progress in Probability (2008)
  • Jonathan Machta, University of Massachusetts Amherst
  • C. M. Newman
  • D. L. Stein
We present extended versions and give detailed proofs of results about percolation (using various sets of two-replica bond occupation variables) in Sherrington-Kirkpatrick spin glasses (with zero external field) that were first given in an earlier paper by the same authors. We also explain how ultrametricity is manifested by the densities of large percolating clusters. Our main theorems concern the connection between these densities and the usual spin overlap distribution. Their corollaries are that the ordered spin glass phase is characterized by a unique percolating cluster of maximal density (normally coexisting with a second cluster of nonzero but lower density). The proofs involve comparison inequalities between SK multireplica bond occupation variables and the independent variables of standard Erdős-Rényi random graphs.
  • Spin glass,
  • percolation,
  • Sherrington-Kirkpatrick model,
  • Fortuin-Kasteleyn,
  • Random graphs
Publication Date
Prepublished version downloaded from ArXiv. Published version is located at
Citation Information
Jonathan Machta, C. M. Newman and D. L. Stein. "Percolation in the Sherrington-Kirkpatrick Spin Glass" Progress in Probability (2008)
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