Abstract

We study the thermodynamics and phase diagrams of two-flavor quantum chromodynamics using the Polyakov-loop extended quark-meson (PQM) model and the Pisarski-Skokov chiral matrix ($\chi M$) model. At temperatures up to $T\approx2T_c$ and baryon chemical potentials up to $\mu_B=400\ \rm{MeV}$, both models show reasonable agreement with the pressure, energy density, and interaction measure as calculated on the lattice. The Polyakov loop is found to rise significantly faster with temperature in models than on the lattice. In the low-temperature and high baryon density regime, the two models predict different states of matter; The PQM model predicts a confined and chirally restored phase, while the $\chi M$ model predicts a deconfined and chirally restored phase. At finite isospin density and zero baryon density, the onset of pion condensation at $T=0$ is at $\mu_I={1\over2}m_{\pi}$, and the transition is second order at all temperatures. The transition temperature for pion condensation coincides with that of the chiral transition for values of the isospin chemical potential larger than approximately $110\ \rm{MeV}$. In the $\chi M$ model they also coincide with the transition temperature for deconfinement. The results are in good overall agreement with recent lattice simulations of the $\mu_I$--$T$ phase diagram.

Highlights

  • The first phase diagram of QCD appeared in the 1970s, and at the time it was thought that it consists of two phases: A hadronic low-temperature phase and a high-temperature phase of deconfined quarks and gluons

  • We study the thermodynamics of two-flavor QCD using the Polyakov-loop extended quark-meson (PQM) model and the Pisarski-Skokov chiral matrix model [1] adapted for two flavors in the mean-field approximation

  • VI, we present the main result of the paper, namely the thermodynamic functions and the phase diagram in the μ-T and μI-T planes

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Summary

INTRODUCTION

The first phase diagram of QCD appeared in the 1970s, and at the time it was thought that it consists of two phases: A hadronic low-temperature phase and a high-temperature phase of deconfined quarks and gluons. An advantage of QCD in a magnetic field or at finite isospin density (but at zero μB) is that there is no sign problem, and one can use standard Monte-Carlo techniques to study the phase diagram of these systems. We study the thermodynamics of two-flavor QCD using the Polyakov-loop extended quark-meson (PQM) model and the Pisarski-Skokov chiral matrix model (χM) [1] adapted for two flavors in the mean-field approximation.

CENTER SYMMETRY AND THE POLYAKOV LOOP
Nc trcLðxÞ: ð7Þ
Nc h trc Tτeig
GLUONIC SECTOR
PQM model
Chiral matrix model
CHIRAL SECTOR
Quark-meson model
A phenomenological quark term
THERMODYNAMICS
Order parameters
Phase diagram
Pion condensation
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