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Activated dynamics: An intermediate model between the random energy model and the p-spin model.

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We introduce the Correlated Random Energy Model (CREM) to study mean-field glass dynamics. The CREM reveals a golf-course-like energy landscape with metabasins, enabling an effective trap model description.

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Area of Science:

  • Statistical Mechanics
  • Complex Systems

Background:

  • Mean-field glasses exhibit slow activated dynamics on timescales dependent on system size (N).
  • Existing models like the Random Energy Model (REM) and p-spin models offer limited perspectives on these dynamics.

Purpose of the Study:

  • Introduce and analyze the Correlated Random Energy Model (CREM) for studying mean-field glass dynamics.
  • Investigate the intermediate regime between REM and p-spin models.
  • Characterize the energy landscape and emergent dynamics of the CREM.

Main Methods:

  • Numerical and analytical studies of the Correlated Random Energy Model (CREM).
  • Characterization of the energy landscape, identifying metabasins.
  • Comparison with existing models like REM and the trap model.

Main Results:

  • The CREM exhibits a complex energy landscape resembling a golf course with metabasins.
  • Each metabasin contains multiple configurations, unlike the REM.
  • An effective description of dynamics emerges when metabasins are mapped to configurations in the trap model.

Conclusions:

  • The CREM provides a valuable framework for interpolating between established models of spin glasses.
  • The identified energy landscape structure and emergent dynamics offer new insights into glassy systems.
  • The study validates the utility of the trap model for describing dynamics in complex energy landscapes.