1998/07/27 by Paulo Murilo Castro de Oliveira, de Oliveira, Paulo Murilo Castro
Physics and Astronomy · #Condensed Matter (cond-mat) #FOS: Physical sciences #cond-mat
paper · pdf · doi:10.48550/arxiv.cond-mat/9807354
10 pages, tex, 1 figure to appear in Eur. Phys. J. B
arxiv created 1998/07/27 · arxiv updated 2009/11/30
The Broad Histogram is a method designed to calculate the energy degeneracy g(E) from microcanonical averages of certain macroscopic quantities Nup and Ndn. These particular quantities are defined within the method, and their averages must be measured at constant energy values, i.e. within the microcanonical ensemble. Monte Carlo simulational methods are used in order to perform these measurements. Here, the mathematical relation allowing one to determine g(E) from these averages is shown to be exact for any statistical model, i.e. any energy spectrum, under completely general conditions. We also comment about some troubles concerning the measurement of the quoted microcanonical averages, when one uses a particular approach, namely the energy random walk dynamics. These troubles appear when movements corresponding to different energy jumps are performed using the same probability, and also when the correlations between successive averaging states are not adequately treated: they have nothing to do with the method itself.