Replica symmetry breaking in the `small world' spin glass
B Wemmenhove, T Nikoletopoulos, J P L Hatchett
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 J long range bonds. Our results agree with numerical simulations significantly better than the replica symmetric (RS) theory.
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