The Nearest and Next Nearest Neighbor Sherrington-Kirkpatrick Model

Details The Nearest and Next Nearest Neighbor Sherrington-Kirkpatrick Model The Nearest and Next Nearest Neighbor Sherrington-Kirkpatrick Model

2001-12-17

arxiv.org/abs/cond-mat/0112316v1

Physics

Condensed Matter

Disordered Systems and Neural Networks

15 pages, 9 figures, Latex file

Scientific paper

The mean field theory of a spin glass with a specific form of nearest and next nearest neighbor interactions is investigated. Depending on the sign of the interaction matrix chosen we either find the continuous replica symmetry breaking seen in the Sherrington-Kirkpartick model or a one step solution similar to that found in structural glasses. Our results are confirmed by numerical simulations and the link between the type of spin-glass behavior and the density of eigenvalues of the interaction matrix is discussed.

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