Phase structure of the linear sigma model with the non-standard symmetry breaking term

Abstract

The phase structure of the linear sigma model at finite isospin chemical potential μ and temperature T is systematically studied in the non-standard case of symmetry breaking by means of the Cornwall–Jackiw–Tomboulis effective potential. The latter quantity is calculated in the improved Hartree–Fock approximation which preserves the Goldstone theorem and the thermodynamic consistency. It results that the charged pions are condensed for μ equal to the pion mass in vacuum and the pion condensation corresponds to a first-order phase transition for 0 ⩽ T ⩽ 175.813 MeV, whereas at higher temperature it becomes a second-order phase transition. Moreover, the chiral-symmetry restoration, which is a first-order phase transition, occurs for 138.464 MeV ⩽ T ⩽ 147.168 MeV. The phase diagrams for both pion and chiral condensates are obtained.