Statistical errors in histogram reweighting

Histogram reweighting methods now play an important role in Monte Carlo simulations, particularly in the study of critical phenomena. Despite this widespread use, a quantitative study of the statistical and systematic errors present when Monte Carlo data are reweighted has been lacking. In this paper, we present a detailed analysis of the statistical errors in histogram reweighting. The formalism is tested with simulations of the d=2 Ising model at infinite temperature and at the critical temperature. The error determined with this formalism agrees well with that calculated in the standard way of analyzing independent histograms. The implications of these results for high-resolution Monte Carlo studies are discussed.