Simulation of a directed random-walk model: the effect of   pseudo-random-number correlations
  We investigate the mechanism that leads to systematic deviations in cluster Monte Carlo simulations when correlated pseudo-random numbers are used. We present a simple model, which enables an analysis of the effects due to correlations in several types of pseudo-random-number sequences. This model provides qualitative understanding of the bias mechanism in a class of cluster Monte Carlo algorithms. 
L.N. Shchur, J.R. Heringa and H.W.J. Bl\"ote