The Friedberg-Lee model at finite temperature and density

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 $B(T,μ)$ 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 $μ=0 \mathrm{MeV}$ and a critical chemical potential $μ\simeq 223.1 \mathrm{MeV}$ 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 $T\leq T_{C}$ (or $μ\leq μ_C$), there is a bag constant $B(T)$ (or $B(T,μ)$) and the soliton solutions are stable. However, when $T>T_{C}$ (or $μ>μ_C$) the bag constant $B(T)=0 \mathrm{MeV}$ (or $B(T,μ)=0 \mathrm{MeV}$) and there is no soliton solution anymore, therefore, the confinement of quarks disappears quickly.