Determining the density of states for classical statistical models by a flat-histogram random walk

Abstract

We describe an efficient and general Monte Carlo algorithm using a flat-histogram random walk to obtain a very accurate estimate of the density of states for classical statistical models. Using this method, we not only can avoid repeating simulations at multiple temperatures but can also estimate the free energy and entropy, quantities which are not directly accessible by conventional Monte Carlo simulations. We apply our algorithm to a spin system to show its accuracy. Since all possible points in the random walk space are visited with the same probability, this algorithm is especially useful for complex systems with rough landscapes such as spin glass models.