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Reduced critical slowing down for statistical physics simulations.

Kurt Langfeld1, Pavel Buividovich2, P E L Rakow2

  • 1School of Mathematics, University of Leeds, Leeds, LS2 9JT, United Kingdom.

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Summary
This summary is machine-generated.

Wang-Landau simulations integrate collective coordinates to mitigate critical slowing down. Using magnetization as a collective coordinate significantly reduces autocorrelation times compared to local updates in Ising model simulations.

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Area of Science:

  • Statistical Mechanics
  • Computational Physics

Background:

  • Wang-Landau simulations enable explicit integration over collective coordinates.
  • Critical slowing down, characterized by large autocorrelation times, hinders simulations.
  • Identifying and integrating collective coordinates can accelerate simulations.

Purpose of the Study:

  • To investigate the efficacy of integrating the "slow mode" as a collective coordinate in Wang-Landau simulations.
  • To analyze the impact of using magnetization as a collective coordinate on critical slowing down in the Ising model.
  • To compare simulation performance with local update algorithms.

Main Methods:

  • Application of Wang-Landau simulations with the linear-log-relaxation (LLR) method.
  • Selection of the "slow mode" and magnetization as collective coordinates.
  • Analysis of autocorrelation times in the Ising model across different system sizes and phases.

Main Results:

  • Supercritical slowing down was observed for heat-bath algorithms in a phase with broken symmetry, showing exponential growth of autocorrelation times.
  • Using magnetization as the collective coordinate eliminated supercritical slowing down.
  • A polynomial increase in autocorrelation time (critical slowing down) was still observed but reduced by orders of magnitude compared to local updates.

Conclusions:

  • Integrating the slow mode, specifically magnetization, as a collective coordinate is an effective strategy to overcome critical slowing down in Wang-Landau simulations.
  • This approach significantly enhances simulation efficiency for models like the Ising model.
  • The findings suggest a generalizable method for accelerating complex system simulations.