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

Abstract

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.

Figures (4)

• Figure 1: Left: The $3$-d, $O(2)$ infinite volume scaling functions $f_G(z)$ and $f_{G\chi}(z)$ versus $z$. Right: The ratio of the $3$-d, $O(2)$ finite volume scaling function $f_{G\chi}(z,z_L)$ and the infinite volume result, $f_{G\chi}(z,0)\equiv f_{G\chi}(z)$, versus $z_L$.
• Figure 2: The scaled order parameter, $M/H^{1/\delta}$, for three values of the light-to-strange quark mass ratio, $H=1/27, 1/40$ and $1/80$, versus the bare finite volume scaling variable $z_{L,b}$.
• Figure 3: Left: The improved order parameter at $T=145.1$ MeV as well as at $T=142.8$ MeV and $T=147.4$ MeV. The latter two data sets have been shifted to the former (see discussion in the text). Right: Aspect ratio $N_\sigma/N_\tau$ needed to reduce finite-volume effects in the improved order parameter $M$ below a certain level, for different light quark masses $m_\ell \equiv m_s H$.
• Figure 4: The infinite volume extrapolated, scaled order parameter versus $H$ for three values of the temperature (blue) and interpolated values (red) used to estimate the chiral phase transition temperature on lattices with temporal extent $N_\tau=8$. Dashed lines show the infinite volume, asymptotic scaling results using the non-universal parameters given in the figure.