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

TL;DR

This paper provides extensive numerical data on the ground states of mean-field spin glasses at low connectivities, serving as benchmarks for theoretical methods and revealing richer phenomena than expected.

Contribution

It offers detailed numerical results for spin glasses on random graphs at low connectivity, testing and verifying replica symmetry breaking techniques and uncovering unexpected phenomenology.

Findings

Verification of replica symmetry breaking techniques.

Discovery of richer phenomenology on fixed-connectivity graphs.

Numerical data supporting potential exact results.

Abstract

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.