Simulations of Ground State Fluctuations in Mean-Field Ising Spin Glasses

TL;DR

This paper investigates how ground-state energy fluctuations in various Ising spin glass models scale with system size, using extensive simulations to understand their asymptotic behavior across different graph structures and interaction types.

Contribution

It provides a comprehensive simulation-based analysis of fluctuation scaling in diverse spin glass models, highlighting differences across interaction types and graph structures.

Findings

Fluctuation scaling varies significantly across models.

Graph bipartitioning exhibits the clearest asymptotic behavior.

Different interaction types (discrete, Gaussian, three-spin) show distinct fluctuation patterns.

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.