Simulations of ground state fluctuations in mean-field Ising spin glasses

Abstract

The scaling of fluctuations in the distribution of ground state energies or costs with the system sizeN for Ising spin glasses is considered using an extensive set of simulations with the extremaloptimization heuristic across a range of different models on sparse and dense graphs. Thesemodels exhibit very diverse behaviors, and an asymptotic extrapolation is oftencomplicated by higher-order corrections in size. The clearest picture, in fact, emerges fromthe study of graph bipartitioning, a combinatorial optimization problem closely related tospin glasses. Asides from two-spin interactions with discrete bonds, we also considerproblems with Gaussian bonds and three-spin interactions, which behave quite differently.