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Equilibrium properties of disordered spin models with two-scale interactions.

Jack Raymond1, David Saad

  • 1Hong Kong University of Science and Technology, Clear Water Bay Road, Clear Water Bay, Hong Kong. jack.raymond@physics.org

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|November 13, 2009
PubMed
Summary

This study introduces a composite spin system model combining sparse and dense interactions. It reveals re-entrant phase transitions and sensitivity to connectivity, advancing disordered spin system understanding.

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Area of Science:

  • Statistical mechanics
  • Condensed matter physics
  • Complex systems

Background:

  • Classical disordered spin systems with idealized structures are well-understood.
  • The Sherrington-Kirkpatrick model (dense interactions) and sparse Erdös-Rényi graphs are established models.
  • Existing models often focus on purely dense or purely sparse interactions.

Purpose of the Study:

  • To investigate the equilibrium properties of a novel composite spin system model.
  • To analyze spin states with a combination of sparse strong and weak dense interactions.
  • To explore phase transitions in this composite model under varying temperatures.

Main Methods:

  • Utilizing the replica method for equilibrium property examination.
  • Applying perturbative schemes for analysis of high-temperature phases (paramagnetic, spin-glass, ferromagnetic).
  • Employing replica symmetric variational approximations for lower-temperature regimes.

Main Results:

  • Demonstrated re-entrant phase transitions from spin-glass to ferromagnetic states as temperature decreases.
  • Observed transitions between replica symmetry broken and replica symmetric phases.
  • Identified that high-temperature transition nature depends on the sparse subgraph's connectivity profile.

Conclusions:

  • The composite spin system exhibits complex phase behaviors, including re-entrance.
  • Perturbative methods have limitations at lower temperatures, necessitating variational approaches.
  • Sparse subgraph connectivity critically influences phase transition characteristics, such as discontinuity.