Bubble nucleation in the two-flavor quark-meson model

We investigate the dynamics of a first-order quark-hadron transition via homogeneous thermal nucleation in the two-flavor quark-meson model. The contribution of the fermionic vacuum loop in the effective thermodynamics potential and phase diagram together with the location of critical end point (CEP) have been obtained in the temperature and chemical potential plane. For a weak and strong first-order phase transition, by taking the temperature as a variable, the critical bubble profiles, the evolutions of the surface tension and the saddle-point action in the presence of a nucleation bubble are numerically calculated in detail when fixing the chemical potentials at $\mu =306\mathrm{M}\mathrm{e}\mathrm{V}$ and $\mu =309\mathrm{M}\mathrm{e}\mathrm{V}$. Our results show that the system could be trapped in the metastable state for a long time as long as the temperature is between the metastable region characterized by the up and low spinodal lines. Moreover, the surface tension at criticality will rise up to about $4\mathrm{M}\mathrm{e}\mathrm{V}\mathrm{/}\mathrm{f}{\mathrm{m}}^2$ when the chemical potential is very high. Such a small value of the surface tension would favor a mixed phase in the cores of compact stars and may have an important implication in astrophysics.