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Dynamical phase transition at κ=0 in sync‑greedy dynamics

Establish that the sync‑greedy dynamics of the Sherrington–Kirkpatrick (SK) model exhibits a dynamical phase transition at κ=0, separating a phase dominated by fully‑rattling 2‑cycles from a phase dominated by convergence to fixed points (1‑cycles) whose energies are close to the ground‑state energy density.

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Background

Forward DMFT analysis defines κ(t) as the κ value minimizing the energy after t steps and shows κ(t) trending to 0 as t increases.

This behavior supports a phase transition at κ=0 between 2‑cycle and 1‑cycle dominated dynamics, consistent with numerical observations.

References

Let us define (t) as the value of κ at which forward DMFT after t steps reaches the minimum energy, and see that as t grows (t) is compatible with lim_{t \to +\infty} (t) = 0, which supports the conjecture that the dynamical phase transition happens at κ \to 0+.

— Quenches in the Sherrington-Kirkpatrick model (2405.04267 - Erba et al., 7 May 2024) in Section 3.1 (Sync-greedy dynamics) — Forward DMFT