Statistical Dependence Analysis

TL;DR

This paper reviews statistical dependence in Monte Carlo simulations, introduces a new method to estimate relaxation times, and applies it to the Ising model to determine the dynamical critical exponent accurately.

Contribution

It presents a novel approach for analyzing statistical dependence and calculating relaxation times in Monte Carlo simulations, improving accuracy in critical dynamics studies.

Findings

Reduced statistical degrees of freedom for correlated data

Finite MC length biases on cumulants discussed

Accurate estimation of the dynamical critical exponent

Abstract

We review our recent studies on the dynamical correlations in MC simulations from the view point of the statistical dependence. Attentions are paid to the reduction of the statistical degrees of freedom for correlated data. Possible biases on several cumulants, such as the susceptibility and the Binder number due to finite MC length are discussed. A new method for calculating the equilibrium relaxation time from the analysis of the statistical dependence is presented. We apply it to the critical dynamics of the Ising model to estimate the dynamical critical exponent accurately.