Chiral soliton model at finite temperature and density

In mean field approximation, we study a chiral soliton of the linear sigma model with two flavors at finite temperature and density. The stable soliton solutions are calculated with some appropriate boundary conditions. Energy and radius of the soliton are determined in a hot medium of constituent quarks. It is found that for $T<T_c$, the energy of the soliton $E^*$ is less than the energy of three constituent quarks $3M_q$, but with the increasing of temperature, the difference between $E^*$ and $3M_q$ becomes smaller and smaller, once $T>T_c$, there is a sharp delocalization phase transition from hadron matter to quark matter coincident with the restoration of chiral symmetry. In the transition region, the thermodynamic properties show large discontinuities which is an indication for a first-order phase transition.

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