Finite-size-scaling functions for 3d O(4) and O(2) spin models and QCD

TL;DR

This paper numerically computes universal finite-size-scaling functions for 3d O(4) and O(2) models, analyzes their approach to infinite-volume behavior, and compares these results with lattice QCD data, revealing similar finite-size effects.

Contribution

It provides the first detailed numerical determination of finite-size-scaling functions for 3d O(4) and O(2) models and compares them with QCD lattice data.

Findings

Finite-size-scaling functions reach asymptotic form at small scaling variables.

Finite-size behavior in QCD lattice data is compatible with spin models.

Finite-size effects are well described by the computed scaling functions.

Abstract

We calculate numerically universal finite-size-scaling functions for the three-dimensional O(4) and O(2) models. The approach of these functions to the infinite-volume scaling functions is studied in detail on the critical and pseudocritical lines. For this purpose we determine the pseudocritical line in two different ways. We find that the asymptotic form of the finite-size-scaling functions is already reached at small values of the scaling variable. A comparison with QCD lattice data for two flavours of staggered fermions shows a similar finite-size behaviour which is compatible with that of the spin models.