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Related Experiment Videos

Phase transition in the ABC model.

M Clincy1, B Derrida, M R Evans

  • 1School of Physics, University of Edinburgh, Mayfield Road, Edinburgh EH9 3JZ, UK.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 26, 2005
PubMed
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This study investigates the ABC model, a one-dimensional driven system. It reveals a second-order phase transition in the disordered state under weak asymmetry, crucial for understanding complex system dynamics.

Area of Science:

  • Statistical Mechanics
  • Condensed Matter Physics
  • Complex Systems

Background:

  • One-dimensional driven systems can exhibit phase separation via local rules.
  • The ABC model shows anomalous coarsening into a phase-separated steady state.
  • Symmetric dynamics (q→1) leads to a disordered steady state without phase separation.

Purpose of the Study:

  • Investigate the approach to the disordered state in the weak asymmetry regime (q=exp(-beta/N)).
  • Analyze the phase transition behavior for equal and unequal particle densities.
  • Determine critical parameters and optimal profiles in the weak asymmetry limit.

Main Methods:

  • Analysis of the ABC model in the weak asymmetry regime.
  • Derivation of the exact large deviation functional.

Related Experiment Videos

  • Development and analysis of mean-field equations for unequal densities.

    • Main Results:

    • A second-order phase transition occurs at a non-zero beta(c) for equal densities.
    • The critical value beta(c) = 2π√(3) was determined.
    • Mean-field equations were derived and analyzed for unequal densities.

    Conclusions:

    • The study elucidates the transition from ordered to disordered states in driven systems.
    • Identifies a critical point and transition mechanism in the ABC model.
    • Provides a theoretical framework for understanding phase separation dynamics in asymmetric systems.