Cluster Monte Carlo: Scaling of Systematic Errors in the 2D Ising Model

TL;DR

This paper analyzes how systematic errors in Wolff cluster simulations of the 2D Ising model depend on simulation parameters, revealing scaling relations that help understand and mitigate these deviations.

Contribution

It provides a detailed analysis of the scaling behavior of systematic errors in cluster Monte Carlo simulations of the 2D Ising model, highlighting the impact of random number generator properties.

Findings

Systematic deviations depend on lattice size, shift-register length, and correlated bits.

Deviations follow specific scaling relations.

Insights into how to reduce errors in Monte Carlo simulations.

Abstract

We present an extensive analysis of systematic deviations in Wolff cluster simulations of the critical Ising model, using random numbers generated by binary shift registers. We investigate how these deviations depend on the lattice size, the shift-register length, and the number of bits correlated by the production rule. They appear to satisfy scaling relations.