Joint Statistics/Physics Colloquium

A New Approach to Monte Carlo Simulations in Statistical Physics and Beyond

Monte Carlo simulations^[1] have become a powerful tool for the study of diverse problems in statistical physics and other areas of science. Traditional Monte Carlo methods sample the probability distribution for the states of the system, most often in the canonical ensemble, and over the past several decades enormous improvements have been made in performance. Nonetheless, difficulties arise near phase transitions due to critical slowing down near 2nd order transitions, to metastability near 1st order transitions, and to "complex metastability" in systems with complex energy landscapes. These complications limit the applicability of "standard" Monte Carlo methods. We shall describe a new Monte Carlo approach^[2] that uses a random walk in energy space to determine the density of states directly. The method is easy to implement and produces remarkably accurate results in an iterative fashion, following a simple recipe. Once the density of states is known, all thermodynamic properties can be calculated at all temperatures from a single simulation. This approach can be extended to multi-dimensional parameter spaces and can be applied to systems with complex energy landscapes, e.g., spin glasses, protein folding models, etc. Generalizations produce broadly applicable optimization tools.

1. A Guide to Monte Carlo Simulations in Statistical Physics, D. P. Landau and K. Binder (Cambridge U. Press, Cambridge, 2000).
2. Fugao Wang and D. P. Landau, Phys. Rev. Lett. 86, 2050 (2001); Phys. Rev. E64, 056101-1 (2001)