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