Physical tests for Random Numbers in Simulations

TL;DR

This paper introduces three physical tests to detect correlations in random numbers used in Monte Carlo simulations, revealing that recent errors stem from short-range correlations in certain algorithms.

Contribution

It presents novel physical tests for identifying correlations in random number sequences used in simulations.

Findings

Identified short-range correlations in random number sequences

Linked correlations to errors in high-precision simulations

Determined the correlation length in tested sequences

Abstract

We propose three physical tests to measure correlations in random numbers used in Monte Carlo simulations. The first test uses autocorrelation times of certain physical quantities when the Ising model is simulated with the Wolff algorithm. The second test is based on random walks, and the third on blocks of n successive numbers. We apply the tests to show that recent errors in high precision simulations using generalized feedback shift register algorithms are due to short range correlations in random number sequences. We also determine the length of these correlations.