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

Abstract

We present modified Wang-Landau algorithm for models with continuous degrees of freedom. We demonstrate this algorithm with the calculation of the joint density of states $g(M,E)$ of ferromagnet Heisenberg models. The joint density of states contains more information than the density of states of a single variable--energy, but is also much more time-consuming to calculate. We discuss the strategies to perform this calculation efficiently for models with several thousand degrees of freedom, much larger than other continuous models studied previously with the Wang-Landau algorithm.

arXiv comment4 pages 4 figures

References in corpus (13)

• An efficient, multiple range random walk algorithm to calculate the density of states
• Determining the density of states for classical statistical models: A random walk algorithm to produce a flat histogram
• On the Wang-Landau Method for Off-Lattice Simulations in the "Uniform" Ensemble
• Understanding and Improving the Wang-Landau Algorithm
• Reconstructing the Density of States by History-Dependent Metadynamics
• Optimizing the ensemble for equilibration in broad-histogram Monte Carlo simulations
• Density of States Monte Carlo Method for Simulation of Fluids
• Avoiding Boundary Effects in Wang-Landau Sampling
• Performance Limitations of Flat Histogram Methods and Optimality of Wang-Landau Sampling
• Wang-Landau sampling for quantum systems: algorithms to overcome tunneling problems and calculate the free energy
• Three-dimensional antiferromagnetic q-state Potts models: application of the Wang-Landau algorithm
• Estimation of critical behavior from the density of states in Classical Statistical Models
• Molecular dynamics simulation of polymer helix formation using rigid-link methods

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