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

We present a modified Wang-Landau algorithm for models with continuous degrees of freedom. We demonstrate this algorithm with the calculation of the joint density of states of ferromagnet Heisenberg models and a model polymer chain. 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 present strategies to significantly speed up this calculation for large systems over a large range of energy and order parameter.

[1]  Gregory Brown,et al.  Wang-Landau estimation of magnetic properties for the heisenberg model , 2005 .

[2]  E. Mastny,et al.  Direct calculation of solid-liquid equilibria from density-of-states Monte Carlo simulations. , 2005, The Journal of chemical physics.

[3]  Chenggang Zhou,et al.  Understanding and improving the Wang-Landau algorithm. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[4]  A. Malakis,et al.  Estimation of critical behavior from the density of states in classical statistical models. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[5]  D. Landau,et al.  A new approach to Monte Carlo simulations in statistical physics: Wang-Landau sampling , 2004 .

[6]  R. Car,et al.  Mapping potential energy surfaces. , 2004, The Journal of chemical physics.

[7]  W. Härdle.  Nonparametric and Semiparametric Models , 2004 .

[8]  A. Laio,et al.  Reconstructing the density of states by history-dependent metadynamics. , 2004, Physical review letters.

[9]  Q. Yan,et al.  Molecular simulation of the reversible mechanical unfolding of proteins. , 2004, The Journal of chemical physics.

[10]  D. Huse,et al.  Optimizing the ensemble for equilibration in broad-histogram Monte Carlo simulations. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[11]  M. Troyer,et al.  Performance limitations of flat-histogram methods. , 2003, Physical review letters.

[12]  J. Pablo,et al.  Density of states simulations of proteins , 2003 .

[13]  K. Binder,et al.  Avoiding boundary effects in Wang-Landau sampling. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[14]  Q. Yan,et al.  Fast calculation of the density of states of a fluid by Monte Carlo simulations. , 2003, Physical review letters.

[15]  M. Troyer,et al.  Flat histogram methods for quantum systems: algorithms to overcome tunneling problems and calculate the free energy. , 2002, Physical review letters.

[16]  Athanassios Z Panagiotopoulos,et al.  Generalization of the Wang-Landau method for off-lattice simulations. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[17]  David P. Landau,et al.  Determining the density of states for classical statistical models by a flat-histogram random walk☆ , 2002 .

[18]  Chiaki Yamaguchi,et al.  Application of new Monte Carlo algorithms to random spin systems , 2002 .

[19]  Juan J. de Pablo,et al.  Monte Carlo simulation of proteins through a random walk in energy space , 2002 .

[20]  D. Rapaport.  Molecular dynamics simulation of polymer helix formation using rigid-link methods. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[21]  J. Pablo,et al.  Density-of-states Monte Carlo method for simulation of fluids , 2002, cond-mat/0201470.

[22]  Y. Okabe,et al.  Three-dimensional antiferromagnetic q-state Potts models: application of the Wang-Landau algorithm , 2001, cond-mat/0108540.

[23]  D. Landau,et al.  Determining the density of states for classical statistical models: a random walk algorithm to produce a flat histogram. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[24]  D. Landau,et al.  Efficient, multiple-range random walk algorithm to calculate the density of states. , 2000, Physical review letters.