Phase Structure of Linear Sigma Model without Neutrality Constraint (I)

Abstract

The pion condensation and chiral phase transition are studied within the linear sigma model with constituent quarks (LSMq). In the chiral limit the pion condensation is always the first-order phase transition and the phase diagrams of the pion condensate are established respectively in the \((\mu,T) , (\mu_I,T)\) and \((\mu_I,\mu)\)-planes, here \(T, \mu\) and \(\mu_I\) are temperature, baryon chemical and isospin chemical potentials. In the physical world, where the chiral symmetry is explicitly broken we investigate systematically the phase structure of pion and chiral condensates in the \((T-\mu-\mu_I)\)-space. The obtained results are mainly compared to the existing data derived from the lattice QCD (LQCD) and the Polyakov-loop extended Nambu-Jona-Lasinio (PNJL) model.