Simulation of a directed random-walk model: the effect of pseudo-random-number correlations

TL;DR

This paper analyzes how correlations in pseudo-random numbers can cause systematic biases in cluster Monte Carlo simulations, providing a simple model to understand these effects.

Contribution

It introduces a simple model to analyze the impact of pseudo-random-number correlations on Monte Carlo simulation bias.

Findings

Correlated pseudo-random numbers can induce systematic deviations in simulations.

The model offers qualitative insights into bias mechanisms in cluster algorithms.

Understanding these effects can improve simulation accuracy.

Abstract

We investigate the mechanism that leads to systematic deviations in cluster Monte Carlo simulations when correlated pseudo-random numbers are used. We present a simple model, which enables an analysis of the effects due to correlations in several types of pseudo-random-number sequences. This model provides qualitative understanding of the bias mechanism in a class of cluster Monte Carlo algorithms.