Strong Ergodicity Breaking in Dynamical Mean-Field Equations for Mixed p-Spin Glasses

Area of Science:

• Statistical Mechanics
• Condensed Matter Physics
• Complex Systems

Background:

• Mean-field spin glasses are crucial for understanding glassy dynamics in diverse physical systems.
• The hypothesis of weak ergodicity breaking, where dynamics wander unbounded and forget configurations, has underpinned analytical solutions.
• Recent numerical simulations and attempts to solve dynamical mean-field equations (DMFEs) have questioned this hypothesis.

Purpose of the Study:

• To investigate the validity of weak ergodicity breaking in out-of-equilibrium spin glass dynamics.
• To explore the nature of aging dynamics in spin glass models beyond current theoretical limitations.
• To provide robust evidence for or against strong ergodicity breaking using advanced computational techniques.

Main Methods:

• Development of a novel integration scheme for solving dynamical mean-field equations (DMFEs).
• Application of the new scheme to the spherical 3+4-spin model, quenching from near mode coupling temperature to zero temperature.
• Achieving very large integration times (t=O(10^6)) to observe long-term dynamics.

Main Results:

• Solid evidence for strong ergodicity breaking in the out-of-equilibrium dynamics of mixed p-spin glass models.
• Demonstration that aging dynamics occur within a restricted space, preserving initial conditions.
• Observation that dynamics evolve towards configurations reached at later times, indicating memory retention.

Conclusions:

• The assumption of weak ergodicity breaking in spin glass dynamics is challenged by strong evidence of restricted aging.
• Out-of-equilibrium dynamics in these models do not lead to complete forgetting of initial states.
• The fluctuation-dissipation relation in this restricted aging regime exhibits unexpected complexity.