Scaling of Pseudo-Critical Couplings in Two-Flavour QCD

TL;DR

This paper investigates the scaling behavior of pseudo-critical couplings in two-flavour QCD, demonstrating universality across different lattice sizes and analyzing the critical exponents related to the chiral phase transition.

Contribution

It shows that lattice simulation results for various lattice sizes can be unified onto a universal scaling curve, supporting second order phase transition behavior with specific critical exponents.

Findings

Results are consistent with $O(4)$ critical exponents.

Scaling behavior observed across different lattice sizes.

Cannot exclude $O(2)$ symmetry group based on current data.

Abstract

We study the scaling behaviour of the pseudo-critical couplings for the chiral phase transition in two-flavour QCD. We show that all existing results from lattice simulations on lattices with temporal extent $N_\tau = 4$, 6 and 8 can be mapped onto a universal scaling curve. The relevant combination of critical exponents, $\beta\delta$, is consistent with the scaling behaviour expected for a second order phase transition with $O(4)$ exponents. At present, scaling according to the $O(2)$ symmetry group can, however, not be ruled out.