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 firstorder phase transition and the phase diagrams of the pion condensate are established respectively in the (µ, T ),(µI , T ) and (µI , µ)-planes, here T, µ and µI 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 −µ−µI )- 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. | Communications in Physics, Vol. 22, No. 1 (2012), pp. 15-31 PHASE STRUCTURE OF LINEAR SIGMA MODEL WITHOUT NEUTRALITY CONSTRAINT (I) TRAN HUU PHAT Vietnam Atomic Energy Commission and Dong Do University NGUYEN VAN THU Institute of Nuclear Science and Technique and Department of Physics, Hanoi University of Education II 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 firstorder phase transition and the phase diagrams of the pion condensate are established respectively in the (µ, T ), (µI , T ) and (µI , µ)-planes, here T, µ and µI 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 −µ−µI )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. I. INTRODUCTION It is known that the study of the phase structure of QCD turns out to be a very hot subject attracted more and more attention, both experimentally and theoretically [1]. Many aspects of in-medium effects such as the chiral restoration at high baryon density, the in-medium properties of hadrons, the pion condensation in dense matter and so on are of special interest. The high energy heavy-ion collisions are presently the powerful machinery to generate hot and dense hadronic matter, and, therefore, they create a good chance for exploring the phase structure of QCD at extreme conditions. It is commonly accepted that the chiral restoration phase transition accompanies the confinement-deconfinement phase transition at the same critical temperature. The recent experimental data of RHIC, collected for high-temperature and low-baryon density region, provide clear signals on the .
