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Hard-disk pressure computations-a historic perspective.

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Accurate pressure calculations for the hard-disk model are crucial for understanding its phase transitions. New Monte Carlo and Metropolis algorithms provide benchmark results for up to one million disks.

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Area of Science:

  • Physics
  • Computational Science

Background:

  • The hard-disk model, a fundamental system in statistical physics, has presented significant challenges in accurately computing its pressure since 1953.
  • The difficulty in pressure estimation has contributed to ongoing debates regarding the hard-disk model's phase-transition scenario.

Purpose of the Study:

  • To present definitive pressure computations for the hard-disk model using advanced algorithms.
  • To introduce new, unbiased pressure estimators and discuss sampling algorithm performance.
  • To provide benchmark data for future research.

Main Methods:

  • Employed a powerful event-chain Monte Carlo algorithm.
  • Utilized a massively parallel Metropolis algorithm for pressure calculations.
  • Developed and tested several new, unbiased pressure estimators.

Main Results:

  • Achieved accurate pressure computations for systems up to one million hard disks.
  • Demonstrated the efficacy of the implemented algorithms and estimators.
  • Identified crucial criteria for bounding mixing times in the absence of analytical predictions.

Conclusions:

  • The study provides reliable benchmark pressure data for the hard-disk model.
  • Highlights the importance of advanced computational methods for resolving long-standing physical model controversies.
  • Makes pressure data, algorithms, and estimators available via an open-source repository.