Replica symmetry breaking in the `small world' spin glass
Disordered Systems and Neural Networks
2015-06-24 v1 Statistical Mechanics
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 M\'ezard & Parisi for the Bethe lattice, we evaluate observables for a model with fixed connectivity and long range bonds. Our results agree with numerical simulations significantly better than the replica symmetric (RS) theory.
Cite
@article{arxiv.cond-mat/0405563,
title = {Replica symmetry breaking in the `small world' spin glass},
author = {B Wemmenhove and T Nikoletopoulos and J P L Hatchett},
journal= {arXiv preprint arXiv:cond-mat/0405563},
year = {2015}
}
Comments
21 pages, 3 figures