A comparison of updating algorithms for large N reduced models

TL;DR

This paper compares different Monte Carlo updating algorithms for simulating large N reduced models of SU(N) Yang-Mills fields, finding that over-relaxation alone efficiently decorrelates observables and is a valid alternative to heat-bath methods.

Contribution

The study demonstrates that over-relaxation updates alone are effective for simulating the TEK model, and compares two implementations, showing similar critical behavior.

Findings

Over-relaxation decorrelates observables faster than heat-bath updates.

Both over-relaxation methods yield the same critical exponent.

Over-relaxation alone is a valid simulation algorithm for the TEK model.

Abstract

We investigate Monte Carlo updating algorithms for simulating $SU(N)$ Yang-Mills fields on a single-site lattice, such as for the Twisted Eguchi-Kawai model (TEK). We show that performing only over-relaxation (OR) updates of the gauge links is a valid simulation algorithm for the Fabricius and Haan formulation of this model, and that this decorrelates observables faster than using heat-bath updates. We consider two different methods of implementing the OR update: either updating the whole $SU(N)$ matrix at once, or iterating through $SU(2)$ subgroups of the $SU(N)$ matrix, we find the same critical exponent in both cases, and only a slight difference between the two.