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Replica symmetry breaking in the `small world' spin glass

B Wemmenhove·T Nikoletopoulos·J P L Hatchett
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Abstract

We apply the cavity method to a spin glass model on a `small world' lattice, a random bond graph super-imposed upon a 1-dimensional ferromagnetic ring. We show the correspondence with a replicated transfer matrix approach, up to the level of one step replica symmetry breaking (1RSB). Using the scheme developed by Mézard & Parisi for the Bethe lattice, we evaluate observables for a model with fixed connectivity and $\pm J$ long range bonds. Our results agree with numerical simulations significantly better than the replica symmetric (RS) theory.

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B Wemmenhove, T Nikoletopoulos, J P L Hatchett. 2004-05-24. Replica symmetry breaking in the `small world' spin glass. https://doi.org/10.1088/1742-5468%2F2005%2F11%2Fp11007

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