We first briefly review importance sampling Monte Carlo methods used in condensed matter physics/materials science and describe a powerful alternative: Wang-Landau sampling. We then introduce a generic, parallel Wang-Landau Monte Carlo method that is naturally suited to implementation on diverse computational facilities ranging from desktop machines to massively parallel, petaflop supercomputers. The approach introduces a replica exchange framework involving densities of states that are determined iteratively for overlapping windows in energy space, each via traditional Wang-Landau sampling. The method is applicable to classical models for materials and to models in which the energy is determined via electronic structure calculation as is often done for T=0 properties. From the density of states, thermodynamic properties of the system can then be determined quite accurately at all temperatures. The advantages and general applicability of the method are demonstrated using thousands of cores for quite different systems (with either discrete or continuous degrees of freedom) including those with complex free energy landscapes and topological constraints.

David P. Landau graduated from Princeton University in 1963, and moved to Yale University where he got his Ph. D in 1967. His research fields cover phase transitions and critical phenomena, interacting many-body systems, computer simulation of condensed matter and biophysical physics. David P. Landau is Distinguished Research Professor of Physics and founding Director of the Center for Simulational Physics at the University of Georgia. He is a Fellow of the American Physical Society. He won the Aneesur Rahman Prize for Computational Physics. This is the highest award in computational physics given by the American Physical Society.