Finite size scaling study of $N_{\text{f}}=4$ finite density QCD on the lattice

TL;DR

This study investigates the nature of the phase transition in 4-flavor lattice QCD at finite density, finding a first order transition at certain parameters that weakens to a crossover at others, using finite size scaling analysis.

Contribution

The paper applies finite size scaling analysis with phase reweighting and Taylor expansion techniques to determine the order of the phase transition in finite density QCD on the lattice.

Findings

First order transition at specific parameters with given mass ratios.

Transition weakens and possibly becomes a crossover at different parameters.

Finite size scaling confirms the nature of the phase transition.

Abstract

We explore the phase space spanned by the temperature and the chemical potential for 4-flavor lattice QCD using the Wilson-clover quark action. In order to determine the order of the phase transition, we apply finite size scaling analyses to gluonic and quark observables including plaquette, Polyakov loop and quark number density, and examine their susceptibility, skewness, kurtosis and Challa-Landau-Binder cumulant. Simulations were carried out on lattices of a temporal size fixed at $N_{\text{t}}=4$ and spatial sizes chosen from $6^3$ up to $10^3$. Configurations were generated using the phase reweighting approach, while the value of the phase of the quark determinant were carefully monitored. The $\mu$-parameter reweighting technique is employed to precisely locate the point of the phase transition. Among various approximation schemes for calculating the ratio of quark determinants needed for $\mu$-reweighting, we found the Taylor expansion of the logarithm of the quark determinant to be the most reliable. Our finite-size analyses show that the transition is first order at $(\beta, \kappa, \mu/T)=(1.58, 0.1385, 0.584\pm 0.008)$ where $(m_\pi/m_\rho, T/m_\rho)=(0.822, 0.154)$. It weakens considerably at $(\beta, \kappa, \mu/T)=(1.60, 0.1371, 0.821\pm 0.008)$ where $(m_\pi/m_\rho, T/m_\rho)=(0.839, 0.150)$, and a crossover rather than a first order phase transition cannot be ruled out.