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Control of accuracy in the Wang-Landau algorithm.

L Yu Barash1,2,3, M A Fadeeva2,3, L N Shchur1,2,3

  • 1Landau Institute for Theoretical Physics, 142432 Chernogolovka, Russia.

Physical Review. E
|January 20, 2018
PubMed
Summary

The Wang-Landau algorithm

Area of Science:

  • Statistical Physics
  • Computational Physics

Background:

  • The Wang-Landau (WL) algorithm is a widely utilized Monte Carlo method for simulations in physics.
  • Accurate estimation of the density of states is crucial for understanding complex systems.

Purpose of the Study:

  • To analyze the properties of the Wang-Landau algorithm.
  • To introduce a method for controlling the accuracy of density of states estimation.

Main Methods:

  • Analysis of the Wang-Landau algorithm's properties.
  • Derivation of analytic expressions for matrix elements in the one-dimensional Ising model.
  • Numerical simulations for one-dimensional and two-dimensional Ising models, and the two-dimensional Potts model.

Main Results:

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  • The difference between the largest eigenvalue of the transition matrix and unity quantifies the accuracy of density of states estimation.
  • Analytic expressions for matrix elements were derived for the 1D Ising model.
  • The proposed method was validated through numerical results.

    • Conclusions:

    • The largest eigenvalue difference provides a controllable parameter for WL algorithm accuracy.
    • The findings are applicable to various statistical physics models, including Ising and Potts models.