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Related Experiment Videos

Directed-loop Monte Carlo simulations of vertex models.

Olav F Syljuåsen1, M B Zvonarev

  • 1NORDITA, Blegdamsvej 17, Copenhagen Ø, DK 2100, Denmark. sylju@nordia.dk

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|August 25, 2004
PubMed
Summary

The directed-loop Monte Carlo algorithm was used to study vertex models, revealing how boundary conditions influence ordered and disordered regions. This research predicts polarization behavior in the thermodynamic limit.

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Area of Science:

  • Statistical Mechanics
  • Computational Physics

Background:

  • Vertex models are fundamental in statistical mechanics.
  • Understanding phase transitions and boundary effects is crucial.

Purpose of the Study:

  • To apply the directed-loop Monte Carlo algorithm to vertex models.
  • To investigate arrow polarization in the six-vertex model with domain wall boundary conditions.

Main Methods:

  • Directed-loop Monte Carlo algorithm.
  • Analysis of the six-vertex model.
  • Domain wall boundary conditions.

Main Results:

  • The algorithm successfully calculates arrow polarization.
  • Spatially separated ordered and disordered regions were observed.

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  • The boundary between these regions is parameter-dependent.

    • Conclusions:

    • The study provides insights into the behavior of polarization near phase boundaries.
    • Predictions for the thermodynamic limit are presented.
    • Connections to the Arctic Circle theorem are discussed.