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 size N for Ising spin glasses is considered using an extensive set of simulations with the Extremal Optimization heuristic across a range of different models on sparse and dense graphs. These models exhibit very diverse behaviors, and an asymptotic extrapolation is often complicated by higher-order corrections. The clearest picture, in fact, emerges from the study of graph-bipartitioning, a combinatorial optimization problem closely related to spin glasses. Aside from two-spin interactions with discrete bonds, we also consider problems with Gaussian bonds and three-spin interactions, which behave differently to a significant degree.