Analytical characterization of single–spin-flip greedy and reluctant dynamics

Develop an analytical characterization of the single–spin-flip greedy and reluctant zero‑temperature dynamics for the Sherrington–Kirkpatrick (SK) model, including a description of their time evolution, convergence properties, and limiting energies.

Background

Although the greedy and reluctant update rules are simple to define, their analysis is challenging because the spin chosen at each step depends on the full, time‑dependent set of local fields, preventing the direct use of standard analytic tools.

A complete analytical treatment would clarify the observed numerical behaviors, such as convergence times and the achieved energies, and relate them to structural properties of the SK energy landscape.