Statistical Dependence and Related Topics

Details Statistical Dependence and Related Topics Statistical Dependence and Related Topics

1994-04-21

arxiv.org/abs/cond-mat/9404066v1

Physics

Condensed Matter

kikuchi@godzilla.kek.jp; LaTeX, 9 pages, 6 figures; to appear in "Computer Simulations in Condensed Matter Physics VII", ed. D

Scientific paper

On the basis of the dynamical interpretation of Monte Carlo simulations, we discuss the relation of the equilibrium relaxation time, the susceptibility and the statistical error. We introduce a new quantity called {\it the statistical dependence time} $\tau_{dep}$, which gives the reduction factor for the statistical degree of freedom due to the dynamical correlations between the data. A new method is proposed for calculating equilibrium relaxation time using $\tau_{dep}$, the method which does not require knowledge of any time-displaced correlation function. We apply this method to the critical dynamics of Ising models in two and three dimensions, and estimate the dynamical critical exponent $z$ precisely. Systematic errors in response functions due to short simulations are also discussed from the viewpoint of the statistical dependence.

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