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Wang-Landau algorithm for continuous models and joint density of states.

Chenggang Zhou1, T C Schulthess, Stefan Torbrügge

  • 1Center for Nanophase Materials Sciences and Computer Science and Mathematics Division, Oak Ridge National Laboratory, Post Office Box 2008, MS6493, Oak Ridge Tennessee, 37831-6493 USA.

Physical Review Letters
|April 12, 2006
PubMed
Summary

We developed a faster Wang-Landau algorithm for complex systems. This method efficiently calculates the joint density of states for models with continuous variables, like magnetic materials and polymers.

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Area of Science:

  • Computational physics
  • Statistical mechanics
  • Materials science

Background:

  • The Wang-Landau algorithm is a powerful Monte Carlo method for calculating the density of states.
  • Calculating the joint density of states (jDOS) provides richer information than single-variable density of states but is computationally intensive.
  • Models with continuous degrees of freedom, such as Heisenberg models and polymer chains, present unique computational challenges.

Purpose of the Study:

  • To present a modified Wang-Landau algorithm suitable for models with continuous degrees of freedom.
  • To demonstrate the algorithm's efficacy in calculating the joint density of states for ferromagnet Heisenberg models and a model polymer chain.
  • To introduce strategies for accelerating the computation of jDOS for large systems across wide energy and order parameter ranges.

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Main Methods:

  • Modification of the Wang-Landau algorithm to handle continuous degrees of freedom.
  • Application of the modified algorithm to calculate the joint density of states for specific physical models.
  • Development and implementation of optimization strategies to enhance computational speed.

Main Results:

  • Successful application of the modified Wang-Landau algorithm to ferromagnet Heisenberg models and a model polymer chain.
  • Demonstration that the joint density of states offers more comprehensive information compared to single-variable density of states.
  • Significant speed-up in the calculation of jDOS for large systems, enabling broader exploration of energy and order parameter space.

Conclusions:

  • The modified Wang-Landau algorithm is an effective tool for studying systems with continuous degrees of freedom.
  • The presented strategies substantially improve the efficiency of joint density of states calculations.
  • This work facilitates more detailed investigations into the statistical properties of complex physical models.