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Permutation glass.

Mobolaji Williams1

  • 1Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA.

Physical Review. E
|February 17, 2018
PubMed
Summary

This study introduces permutation glasses, a new disordered system model. It finds that these systems transition to correctly ordered states at lower temperatures than non-disordered systems, with accessibility depending on energy favorability.

Area of Science:

  • Statistical physics
  • Disordered systems
  • Complex systems

Background:

  • Disordered systems exhibit novel phases due to competing thermal and nonthermal disorder.
  • Order parameter behavior in these systems is nontrivial.
  • Existing models often involve spin glasses with disorder in Hamiltonian parameters.

Purpose of the Study:

  • Introduce a new disordered system model: permutation glasses.
  • Analyze the thermal behavior of order parameters in permutation glasses.
  • Investigate conditions for accessing the correctly ordered state.

Main Methods:

  • Modeling disordered systems with permutation orderings.
  • Analyzing energy costs using Gaussian, uniform, and Bernoulli distributions.

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  • Employing Jensen's inequality to derive conditions.
  • Utilizing a replica symmetric ansatz for analysis.
  • Main Results:

    • Permutation glasses transition to the correctly ordered state at temperatures lower than non-disordered systems.
    • Accessibility of the correctly ordered state requires specific probabilities of energetically favored incorrect orderings.
    • Results are consistent with a replica symmetric ansatz.
    • No distinct permutation glass phase identified in the simplest model.

    Conclusions:

    • Introduces exactly soluble models for statistical mechanics.
    • Provides a framework for investigating statistical models of disorder.
    • Suggests potential extensions to more complex Hamiltonians for novel phase behavior.
    • Highlights a correspondence with discrete-energy-level fermion gas models.