The Friedberg-Lee model at finite temperature and density

TL;DR

This paper investigates the Friedberg-Lee model at finite temperature and density, calculating the effective potential, bag constant, and soliton solutions, revealing critical points where quark confinement ceases.

Contribution

It provides a detailed analysis of the Friedberg-Lee model's behavior at finite temperature and density, including the calculation of critical parameters and soliton stability.

Findings

Identifies a critical temperature T_C ≈ 106.6 MeV at zero chemical potential.

Finds a critical chemical potential μ_C ≈ 223.1 MeV at T=50 MeV.

Shows soliton solutions are stable below T_C and μ_C, but vanish above these thresholds.

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 $T\leq T_{C}$ (or $\mu \leq \mu_C$), 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.