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 $T_C\simeq 106.6$ MeV when $\mu =0$ MeV and a critical chemical potential $\mu \simeq 223.1$ MeV for fixing the temperature at $T=50$ MeV. We also calculate the soliton solutions of the Friedberg-Lee model at finite temperature and density. It turns out that when $T⩽T_C$ (or $\mu ⩽{\mu }_C$), 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 $B(T)=0$ MeV [or $B(T,\mu )=0$ MeV] and there is no soliton solution anymore, therefore, the confinement of quarks disappears quickly.

• Received 2 December 2007

DOI:https://doi.org/10.1103/PhysRevC.77.065205