Asymptotic fate of the finite-time crossover

Determine whether the finite-time crossover observed in coupled spherical p-spin dynamics becomes a sharp transition in the asymptotic long-time limit.

Background

The study compares finite-time dynamical measurements with marginal one-step and two-step replica-symmetry-breaking predictions for two coupled spherical p-spin systems. In the accessible numerical time window, the authors observe a crossover between dynamical regimes, but the available numerical accuracy and integration horizon do not establish whether this crossover persists as a genuine sharp transition at asymptotically long times.