The Friedberg-Lee model at finite temperature and density

Abstract

The Friedberg-Lee model is studied at finite temperature and density. By using the finite temperature field theory, the effective potential of the Friedberg-Lee model and the bag constant $B(T)$ and $B(T,\mu )$ have been calculated at different temperatures and densities. It is shown that there is a critical temperature $T_C\simeq 106.6\mathrm{MeV}$ when $\mu =0\mathrm{MeV}$ and a critical chemical potential $\mu \simeq 223.1\mathrm{MeV}$ for fixing the temperature at $T=50\mathrm{MeV}$. We also calculate the soliton solutions of the Friedberg-Lee model at finite temperature and density. It turns out that when $T\le T_C$ (or $\mu \le {\mu }_C$), there is a bag constant $B(T)$ (or $B(T,\mu )$) and the soliton solutions are stable. However, when $T>T_C$ (or $\mu >{\mu }_C$) the bag constant $B(T)=0\mathrm{MeV}$ (or $B(T,\mu )=0\mathrm{MeV}$) and there is no soliton solution anymore, therefore, the confinement of quarks disappears quickly.

Comments: 12 pages, 11 figures; version accepted for publication in Phys. Rev. C