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Transition path sampling algorithm for discrete many-body systems.

Thierry Mora1, Aleksandra M Walczak, Francesco Zamponi

  • 1Laboratoire de Physique Statistique, UMR 8550, CNRS and Ecole Normale SupĂ©rieure, 24 Rue Lhomond, 75231 Paris Cedex 05, France.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|May 17, 2012
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Summary
This summary is machine-generated.

We developed a new Monte Carlo method for simulating systems with fixed start and end points. This approach efficiently calculates transition rates in complex systems, including those out of equilibrium.

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Area of Science:

  • Computational Physics
  • Statistical Mechanics
  • Stochastic Processes

Background:

  • Simulating complex systems with discrete degrees of freedom often requires efficient methods for sampling trajectories.
  • Calculating transition rates in systems, especially those out of equilibrium, presents significant computational challenges.

Purpose of the Study:

  • To introduce a novel Monte Carlo method for efficiently sampling trajectories with fixed initial and final conditions.
  • To enable the calculation of transition rates in diverse stochastic processes, including non-equilibrium systems.

Main Methods:

  • A new path sampling algorithm based on Monte Carlo techniques is proposed.
  • The algorithm is combined with thermodynamic integration for accurate transition rate calculations.
  • The method is applied to the two-dimensional Ising model with periodic boundary conditions.

Main Results:

  • The proposed method demonstrates efficient trajectory sampling for systems with fixed endpoints.
  • Calculated transition rates show agreement with established results for the Ising model across various system sizes.
  • The computational approach exhibits good scalability with increasing system size.

Conclusions:

  • The developed Monte Carlo method provides an efficient and scalable approach for simulating complex systems.
  • This technique offers valuable complementary information to existing algorithms for studying systems out of equilibrium.
  • The method is broadly applicable to stochastic processes with local interactions.