B Wemmenhove, T Nikoletopoulos, J P L Hatchett
Published 2004-05-24Version 1
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 M\'ezard & 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.
Comments: 21 pages, 3 figures
The spherical $2+p$ spin glass model: an exactly solvable model for glass to spin-glass transition
Ground-state topology of the Edwards-Anderson +/-J spin glass model
A spin glass model for reconstructing nonlinearly encrypted signals corrupted by noise
