Comparison of finite-size-scaling functions for 3d O(N) spin models to QCD

TL;DR

This study numerically computes universal finite-size-scaling functions for 3D O(4) and O(2) spin models and compares them with QCD lattice data, revealing similar finite-size behaviors.

Contribution

It provides detailed numerical analysis of finite-size-scaling functions for 3D O(N) models and compares these with QCD lattice results, highlighting their compatibility.

Findings

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

Finite-size behavior of QCD data is compatible with O(N) spin models.

Finite-size effects are well-characterized on critical and pseudocritical lines.

Abstract

We calculate numerically universal finite-size-scaling functions of the magnetization for the three-dimensional O(4) and O(2) spin 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.