Explain why reluctant single–spin-flip quenches outperform greedy in SK

Determine a theoretical explanation and rigorous conditions under which the reluctant single–spin-flip zero‑temperature quench for the Sherrington–Kirkpatrick (SK) model reaches lower energies at convergence than the greedy (and random/sequential) single–spin-flip dynamics, and ascertain the extent to which this advantage holds in the thermodynamic limit.

Background

In the SK model, several single–spin-flip zero‑temperature quenches are considered, notably the greedy, random/sequential, and reluctant updates. Empirically, the reluctant dynamics attains substantially lower energies at convergence than the greedy one, despite making the smallest possible energy drop at each step.

Understanding the mechanism behind this counterintuitive phenomenon and delineating its scope is important both for spin-glass dynamics and for broader optimization heuristics inspired by such dynamics.