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Lifted worm algorithm for the Ising model.

Eren Metin Elçi1, Jens Grimm2, Lijie Ding3

  • 1School of Mathematical Sciences, Monash University, Clayton, Victoria 3800, Australia.

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Summary
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A new irreversible worm algorithm enhances dynamic critical behavior analysis for the Ising model. This lifted worm algorithm shows improved performance on complete graphs and toroidal grids compared to reversible methods.

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Area of Science:

  • Statistical mechanics
  • Computational physics
  • Dynamical systems

Background:

  • The ferromagnetic Ising model is a fundamental model in statistical mechanics.
  • Understanding dynamic critical behavior is crucial for characterizing phase transitions.
  • Existing reversible worm algorithms have limitations in efficiency.

Purpose of the Study:

  • To develop an irreversible worm algorithm for the zero-field ferromagnetic Ising model.
  • To investigate the dynamic critical behavior of an energylike observable.
  • To compare the performance of the new algorithm against established reversible methods.

Main Methods:

  • Utilizing the lifting technique to design an irreversible worm algorithm.
  • Simulating the Ising model on complete graphs and toroidal grids.
  • Analyzing the dynamic critical exponent of an energylike observable.

Main Results:

  • The lifted worm algorithm demonstrates improved dynamic exponent on complete graphs.
  • A significant constant improvement in performance was observed on toroidal grids.
  • Comparison with the Prokof'ev-Svistunov worm algorithm highlights the advantages of the irreversible approach.

Conclusions:

  • The irreversible lifted worm algorithm is an effective method for studying dynamic critical phenomena.
  • This approach offers enhanced efficiency for simulations of the Ising model.
  • The findings contribute to the development of advanced computational techniques in statistical physics.