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Gauge symmetries and percolation in ±J Ising spin glasses
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  • Published: February 1999

Gauge symmetries and percolation in ±J Ising spin glasses

  • Christian Mazza1 

Probability Theory and Related Fields volume 113, pages 171–190 (1999)Cite this article

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Abstract.

We consider the ±J spin glass on a finite graph G=(V,E), with i.i.d. couplings. Our approach considers the Z 2 local gauge invariance of the system. We see the gauge group as a graph theoretic linear code ? over GF(2). The gauge is fixed by choosing a convenient linear supplement of ?. Assuming some relation between the disorder parameter p and the inverse temperature of the thermal bath β pb , we study percolation in the random interaction random cluster model, and extend the results to dilute spin glasses.

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  1. Section de Mathématiques, 2-4 Rue du Lièvre, Case Postale 240, CH-1211 Genève 24 Switzerland. e-mail: mazza@sc2a.unige.ch, , , , , , CH

    Christian Mazza

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  1. Christian Mazza
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Received: 5 May 1997 / Revised version: 9 April 1998

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Mazza, C. Gauge symmetries and percolation in ±J Ising spin glasses. Probab Theory Relat Fields 113, 171–190 (1999). https://doi.org/10.1007/s440-1999-8032-8

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  • Issue Date: February 1999

  • DOI: https://doi.org/10.1007/s440-1999-8032-8

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  • "Mathematics Subject Classification (1991): 60K35, 05C80, 82B43, 82B44, 82D30
  • Key words: Spin glasses – Hopfield neural networks – Graph theoretic codes – Local gauge invariance – Percolation – Random interaction random cluster measure
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