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Methods of Ex Situ and In Situ Investigations of Structural Transformations: The Case of Crystallization of Metallic Glasses
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Long-time predictability in disordered spin systems following a deep quench.

J Ye1, R Gheissari2, J Machta3

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Summary
This summary is machine-generated.

Predictability in spin systems depends on initial conditions. For most systems, initial state influence decays with increasing dimension or system size, but not in mean-field models.

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Area of Science:

  • Statistical Mechanics
  • Condensed Matter Physics

Background:

  • Investigating predictability in disordered Ising spin systems at zero temperature.
  • Understanding the balance between initial state information and system history.

Purpose of the Study:

  • Quantify the influence of initial states on final states in spin systems.
  • Explore how dimensionality and system size affect predictability.

Main Methods:

  • Numerical studies of the dynamical order parameter in Edwards-Anderson and Sherrington-Kirkpatrick models.
  • Analytical studies of mean-field models (random energy model, Curie-Weiss ferromagnets).

Main Results:

  • Initial state influence decays with increasing dimension in short-range systems.
  • Initial state influence decays with increasing spin number in infinite-range systems.
  • Mean-field models retain initial state information in the thermodynamic limit.

Conclusions:

  • Conjecture that initial state influence decays to zero in finite-dimensional systems as dimension approaches infinity.
  • Frustration significantly alters dynamics and predictability in mean-field models, unlike short-range systems.