Systematic errors due to linear congruential random-number generators with the Swendsen-Wang algorithm: A warning

TL;DR

This paper reveals that linear congruential pseudo-random-number generators can introduce significant systematic errors in Monte Carlo simulations with the Swendsen-Wang algorithm, especially under specific lattice and update conditions, but these errors can be mitigated by altering update procedures and using better generators.

Contribution

The study identifies the source of systematic errors caused by linear congruential generators in the Swendsen-Wang algorithm and proposes practical solutions to reduce these errors.

Findings

Systematic errors occur when lattice size is a multiple of a large power of 2 and one random number per bond is used.

Updating bonds in a random or aperiodic order reduces systematic errors.

Using generators with larger modulus (60 bits or more) mitigates errors.

Abstract

We show that linear congruential pseudo-random-number generators can cause systematic errors in Monte Carlo simulations using the Swendsen-Wang algorithm, if the lattice size is a multiple of a very large power of 2 and one random number is used per bond. These systematic errors arise from correlations within a single bond-update half-sweep. The errors can be eliminated (or at least radically reduced) by updating the bonds in a random order or in an aperiodic manner. It also helps to use a generator of large modulus (e.g. 60 or more bits).