Finite-volume effects on phase transition in the Polyakov-loop extended Nambu-Jona-Lasinio model with a chiral chemical potential

TL;DR

This paper studies how finite-volume effects influence phase transitions in a QCD-inspired model with a chiral chemical potential, revealing significant shifts in critical points and phase diagram topology relevant for heavy-ion collision experiments.

Contribution

It introduces a chiral chemical potential into the Polyakov-loop extended Nambu-Jona-Lasinio model to analyze finite-volume effects on phase transitions and critical end points.

Findings

Chiral chemical potential does not alter critical exponents.

Finite volume shifts the critical end point location significantly.

Critical end point disappears below a minimum system size.

Abstract

To investigate finite-volume effects on the chiral symmetry restoration and the deconfinement transition and some impacts of possible global topological background for a quantum chromodynamics (QCD) system with $N_f=2$ (two quark flavors), we apply the Polyakov-loop extended Nambu-Jona-Lasinio model by introducing a chiral chemical potential $\mu_5$ artificially. The final numerical results indicate that the introduced chiral chemical potential does not change the critical exponents but shifts the location of critical end point (CEP) significantly; the ratios for the chiral chemical potentials and temperatures at CEP, $\mu_c/\mu_{5c}$ and $T_c/T_{5c}$, are significantly affected by the system size $R$. The behavior is that $T_c$ increases slowly with $\mu_5$ when $R$ is large and $T_c$ decreases first and then increases with $\mu_5$ when $R$ is small. It is also found that for a fixed $\mu_5$, there is a $R_{\text{min}}$, where the critical end point vanishes, and the whole phase diagram becomes a crossover when $R<R_{\text{min}}$. Therefore, we suggest that for the heavy-ion collision experiments, which is to study the possible location of CEP, the finite-volume behavior should be taken into account.