Particle density in zero temperature symmetry restoring phase transitions in four-fermion i.pdf

a r X i v : h e p - t h / 0 3 0 8 1 3 9 v 1 2 1 A u g 2 0 0 3 Particle density in zero temperature symmetry restoring phase transitions in four-fermion interaction models? Zhou Bang-Rong Department of Physics, Graduate School of the Chinese Academy of Sciences, Beijing 100039, China and CCAST (World Lab.),P.O. 8730, Beijing 100080, China Abstract By means of critical behaviors of the dynamical fermion mass in four-fermion interaction models, we have shown by explicit calculations that when T = 0 the particle density will have a discontinuous jumping across the critical chemical potential μc in 2D and 3D Gross-Neveu (GN) model and these physically explain the first order feature of corresponding symmetry restoring phase transitions. For second order phase transitions in 3D GN model when T → 0 and in 4D Nambu-Jona-Lasinio (NJL) model when T = 0, it has been proven that the particle density itself will be continuous across μc but its derivative over the chemical potential μ will have a discontinuous jumping. The results give a physical explanation of implications of the tricritical point (T, μ) = (0, μc) in 3D GN model. The discussions also show effectiveness of the critical analysis approach of phase transitions. PACS numbers : 11.10.Wx; 12.40.-y;11.30.Qc Key words : Gross-Neveu and Nambu-Jona-Lasinio model, symmetry restoration at zero temperature and high density, particle number density, first and second order phase transition 1 Introduction Four-fermion interaction models [1, 2] are good laboratories to research dynamical symmetry restoring phase transitions at high temperature and high density [3, 4, 5]. It has been proven that when temperature T goes to zero, the feature of the phase transitions in these models strongly depend on dimension D of time-space [6, 7, 8]. It is shown that that the symmetry restoring phase transitions at high fermion chemical potential μ and T = 0 are first order when D = 2 and D = 3 however second order when D = 4 and the momentu