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Isochronal sampling in non-Boltzmann Monte Carlo methods.

Charlles R A Abreu1

  • 1School of Chemical Engineering, State University of Campinas, Campinas, Sao Paulo 13083-970, Brazil. abreu@feq.unicamp.br

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Non-Boltzmann sampling methods improve Monte Carlo simulations by broadening parameter ranges. A new discrete-parameter extension ensures equal uptrip and downtrip times, enhancing robustness and applicability in complex systems.

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Area of Science:

  • Computational Physics
  • Statistical Mechanics
  • Molecular Dynamics

Background:

  • Conventional Monte Carlo methods often face ergodicity issues.
  • Non-Boltzmann sampling (NBS) methods broaden sampling ranges for order parameters like energy.
  • Previous NBS methods focused on uniform sampling, but optimal strategies minimize roundtrip times.

Purpose of the Study:

  • To prove that minimizing roundtrip times in NBS also equalizes uptrip and downtrip times.
  • To propose a discrete-parameter extension of NBS methods with isochronal (equal time) character.
  • To assess the robustness and applicability of the new method compared to existing approaches.

Main Methods:

  • Theoretical proof of isochronal properties for roundtrip time minimization.
  • Development and implementation of a discrete-parameter NBS extension.
  • Simulations of spin systems and lattice chains exhibiting folding transitions.

Main Results:

  • The proposed discrete-parameter method achieves isochronal sampling.
  • The new method performs comparably to the Trebst et al. method when applicable.
  • The new method demonstrates greater robustness, handling cases where the original method is inapplicable.

Conclusions:

  • The developed discrete-parameter NBS method is a robust extension that ensures isochronal sampling.
  • This approach offers advantages in systems where the order parameter or Monte Carlo moves limit the applicability of previous methods.
  • An interesting connection exists between this work and committor analysis in molecular simulation.