STATISTICAL DEPENDENCE TIME AND ITS APPLICATION TO DYNAMICAL CRITICAL EXPONENT

A new method for studying dynamical correlation of temporal sequence is proposed. We introduce a new quantity named statistical dependence time tau(dep) as an estimator for the equilibrium relaxation time. The calculation of tau(dep), does not require calculation of any time-displaced correlation function nor numerical fitting in extracting the relaxation time; as a result, the estimation of tau(dep) and statistical analysis such as the error estimation are quite straightforward and simple. We apply this method to the critical dynamics of 3D Ising model, and estimate the dynamical critical exponent z as 2.030+/-0.004, provided K(c)=0.221654 (if possible error in K(c) is taken into account, the error in z becomes 0.01).