Errors in Monte Carlo simulations using shift register random number generators

TL;DR

This paper identifies significant systematic errors in Monte Carlo simulations caused by correlations in shift register random number generators, especially affecting large systems with specific sizes, impacting the accuracy of critical property measurements.

Contribution

It reveals the source of large systematic errors in Monte Carlo simulations using shift register generators and highlights conditions under which these errors occur.

Findings

Systematic errors manifest as 20% asymmetry in magnetisation distribution.

Errors are linked to the interplay between generator correlations and large clusters.

Errors depend on system size being a multiple of the generator's lag parameter.

Abstract

We report large systematic errors in Monte Carlo simulations of the tricritical Blume-Capel model using single spin Metropolis updating. The error, manifest as a $20\%$ asymmetry in the magnetisation distribution, is traced to the interplay between strong triplet correlations in the shift register random number generator and the large tricritical clusters. The effect of these correlations is visible only when the system volume is a multiple of the random number generator lag parameter. No such effects are observed in related models.