Wang-Landau sampling with logarithmic windows for continuous models

We present a modified Wang-Landau sampling (MWLS) for continuous statistical models by partitioning the energy space into a set of windows with logarithmically shrinking width. To demonstrate its necessity and advantages, we apply this sampling to several continuous models, including the two-dimensional square XY spin model, triangular J1-J2 spin model, and Lennard-Jones cluster model. Given a finite number of bins for partitioning the energy space, the conventional Wang-Landau sampling may not generate sufficiently accurate density of states (DOS) around the energy boundaries. However, it is demonstrated that much more accurate DOS can be obtained by this MWLS, and thus a precise evaluation of the thermodynamic behaviors of the continuous models at extreme low temperature (kBT<0.1) becomes accessible. The present algorithm also allows efficient computation besides the highly reliable data sampling.