Numerical Results for Ground States of Mean-Field Spin Glasses at low Connectivities

Details Numerical Results for Ground States of Mean-Field Spin Glasses at low Connectivities Numerical Results for Ground States of Mean-Field Spin Glasses at low Connectivities

2002-08-23

arxiv.org/abs/cond-mat/0208444v1

Physical Review B 67, Rapid Communications 060403 (2003)

Physics

Condensed Matter

Disordered Systems and Neural Networks

4 pages, RevTex4, 5 ps-figures included, related papers available at http://www.physics.emory.edu/faculty/boettcher/

Scientific paper

10.1103/PhysRevB.67.060403

An extensive list of results for the ground state properties of spin glasses on random graphs is presented. These results provide a timely benchmark for currently developing theoretical techniques based on replica symmetry breaking that are being tested on mean-field models at low connectivity. Comparison with existing replica results for such models verifies the strength of those techniques. Yet, we find that spin glasses on fixed-connectivity graphs (Bethe lattices) exhibit a richer phenomenology than has been anticipated by theory. Our data prove to be sufficiently accurate to speculate about some exact results.

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