Directed random walks and global updates for improved convergence in multicanonical Monte Carlo algorithms*

Modern Monte Carlo algorithms such as multicanonical sampling and Wang-Landau sampling are robust methods to obtain the density of states for physical systems. However, they require a long time to converge, making them computationally expensive. We propose a novel scheme to achieve faster convergence and improve the efficiency of these algorithms. By performing a global update of the sampling weights across the phase space, the algorithm achieves uniform sampling quickly. Combining this global update scheme with the recently proposed histogram-free multicanonical method [1,2], we have observed three orders of magnitude of speedup compared to existing flat-histogram methods on Heisenberg models and a homopolymer model.
[1] Y. W. Li and M. Eisenbach, in Proceedings of PASC ’17, Association for Computing Machinery, New York, NY, USA, Article 10 (2017).
[2] A. C. K. Farris, Y. W. Li and M. Eisenbach, Comput. Phys. Comm., in press (https://doi.org/10.1016/j.cpc.2018.09.025).