Universal and non-universal finite-volume effects in the vicinity of chiral phase transition in (2+1)-flavor QCD

In this proceeding, we discuss the finite-size scaling analysis of the order parameter related to the chiral phase transition in QCD with two massless quarks. We use data obtained in lattice QCD calculations performed with highly improved staggered quarks (HISQ) for a range of light quark masses, $1/240 \leq m_\ell/m_s \leq 1/27$ for different spatial volumes ($N_σ$) on Euclidean lattices with temporal extent $N_τ=8$, satisfying $3,N_τ\leq N_σ\leq 10,N_τ$. We observe that infinite volume extrapolated data for the order parameter agree reasonably well with the expected $O(2)$ scaling behavior even for physical ratios of the light-to-strange quark mass ratio. We quantify deviations from asymptotic scaling and perform a detailed analysis of the influence of finite-size effects in terms of temperature and quark masses at a fixed lattice cutoff. This is crucial for improving the reliability of the infinite-volume extrapolated estimate of the chiral order parameter and for a more precise determination of chiral phase transition temperature from direct Lattice QCD simulations.

💡 Research Summary

In this work the authors investigate finite‑volume effects and universal scaling near the chiral phase transition of (2+1)‑flavor QCD using highly improved staggered quarks (HISQ). Simulations are performed on lattices with temporal extent Nτ=8 and spatial sizes ranging from 3 Nτ to 10 Nτ, covering a wide range of light‑to‑strange quark mass ratios H=mℓ/ms from 1/240 up to the physical value 1/27. The chiral condensate and its susceptibility are combined into a renormalization‑group invariant order parameter M=⟨ψ̄ψ⟩ℓ−Hχℓ, which is rendered dimensionless by the kaon decay constant fK. Near the critical point the authors employ finite‑size scaling theory: M=H1/δ fG(z,zL) and χ=H−1/δ fχ(z,zL), where the scaling variables z∝τ H−1/βδ and zL∝L−1 H−ν/βδ encode reduced temperature τ=(T−Tc)/Tc, the aspect ratio L=Nσ/Nτ, and the symmetry‑breaking field H. The critical exponents β=0.34864, δ=4.7798, and ν (derived from hyperscaling) correspond to the three‑dimensional O(2) universality class, which is appropriate for staggered fermions at finite lattice spacing.

The authors adopt the parametrization of the O(2) scaling functions from Ref.