 
Summary: Determining the density of states for classical statistical models:
A
random walk algorithm to produce a flat histogram
Fugao Wang and D. P. Landau
Center for Simulational Physics, The University of Georgia, Athens, Georgia 30602
¡Received 22 February 2001; revised manuscript received 27 June 2001; published 17 October 2001¢
We
£ describe an efficient Monte Carlo algorithm using a random walk in energy space to obtain a very
accurate¤ estimate of the density of states for classical statistical models. The density of states is modified at
each¥ step when the energy level is visited to produce a flat histogram. By carefully controlling the modification
factor,
¦ we allow the density of states to converge to the true value very quickly, even for large systems. From
the
§ density of states at the end of the random walk, we can estimate thermodynamic quantities such as internal
energy¥ and specific heat capacity by calculating canonical averages at any temperature. Using this method, we
not only can avoid repeating simulations at multiple temperatures, but we can also estimate the free energy and
entropy,¥ quantities that are not directly accessible by conventional Monte Carlo simulations. This algorithm is
especially¥ useful for complex systems with a rough landscape since all possible energy levels are visited with
the
§ same probability. As with the multicanonical Monte Carlo technique, our method overcomes the tunneling
