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Event-chain Monte Carlo with factor fields.

Ze Lei1, Werner Krauth1, A C Maggs2

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Event-chain Monte Carlo (ECMC) with factor fields significantly enhances simulation efficiency for 1D particle systems. This improved ECMC method drastically reduces autocorrelation times, enabling faster equilibrium attainment in simulations.

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Area of Science:

  • Computational physics
  • Statistical mechanics
  • Particle dynamics

Background:

  • Traditional Monte Carlo methods can exhibit slow dynamics in simulating interacting particle systems.
  • Previous event-chain Monte Carlo (ECMC) algorithms faced challenges with factor potential mismatches in 1D systems.

Purpose of the Study:

  • To address the limitations of existing ECMC algorithms in one-dimensional (1D) systems.
  • To introduce and validate a novel ECMC approach utilizing factor fields for improved simulation efficiency.

Main Methods:

  • Simulation of 1D interacting particle systems using the event-chain Monte Carlo (ECMC) algorithm.
  • Implementation and testing of ECMC with factor fields on harmonic, Lennard-Jones, and hard sphere models.
  • Analysis of autocorrelation and mixing times as a function of system size.

Main Results:

  • ECMC with factor fields effectively overcomes the factor potential mismatch issue in 1D.
  • Autocorrelation times in simulations scale with the square root of system size, a significant improvement over existing methods.
  • Mixing times exhibit a linear scaling with system size.

Conclusions:

  • ECMC with factor fields offers a substantial speedup for simulating 1D particle dynamics.
  • This method provides a more efficient approach for reaching equilibrium in complex 1D systems.
  • The findings are applicable to various physical models including harmonic, Lennard-Jones, and hard spheres.