Journal of Statistical Physics, Vol. 122, No. 3, February 2006. p. 511-529.
DOI: 10.1007/s10955-005-8016-8
The flat histogram Monte Carlo algorithms have been successfully used in many problems in scientific computing.However, there is no a rigorous theory for the convergence of the algorithms. In this paper, a modified flat histogram algorithm is presented and its convergence is studied. The convergence of the multicanonical algorithm and the Wang-Landau algorithm is argued based on their relations to the modified algorithm. The numerical results show the superiority of the modified algorithm to the multicanonical and Wang-Landau algorithms.