Broad Histogram Method

Abstract

Ferrenberg and Swendsen histogram method is based on Boltzmann probability distribution which presents exponentially decaying tails. Thus, it gives accurate measures only within a narrow window around the simulated temperature. The larger the system, the narrower this window, and the worst the performance of this method. We present a quite different approach, defining a non-biased random walk along the E axis with long range power-law decaying tails, and measuring directly the degeneracy g(E), without thermodynamic constraints. Our arguments are general (model independent), and the method is shown to be exact for the 1D Ising ferromagnet. Also for the 2D Ising ferromagnet, our numerical results for different thermodynamic quantities agree quite well with exact expressions.