constant and $\omega$ a weight coefficient. By fitting two-flavor lattice results from [@Burger2013The], we take $C_p = -0.25, g_p=0.86.$

=6.5 cm =4.5 cm =6.5 cm =4.5 cm -0.05cm 0.15 cm **( a )** 6.5 cm **( b )**\

The expectation value for the Polyakov loop $\langle L\rangle$ at the chemical potentials $\mu = 0$ and $\mu = 0.5  {\rm GeV}$ are given in Fig.\[L\_mu0\_mu05\](a). We can see that at low temperature the system is in confined phase with large $\langle L \rangle$, while at large temperature it tends to zero showing a deconfinement phase transition. The transition from the confined phase to the deconfined phase is smooth, showing a crossover type transition. Usually, one can extract the corresponding pseudo critical temperatures through the derivative of $\frac{d \langle L\rangle}{dT}$, and the location of the peak gives the pseudo critical temperature. In Fig.\[L\_mu0\_mu05\](b), the results for $\frac{d \langle L\rangle}{dT}$ are given, which shows a weak dependence of critical temperature on the chemical potential. We then calculate the temperature dependent Polyakov loop up to the chemical potential $\mu=0.8 \rm{GeV}$, and obtain the $T - \mu$ phase diagram for deconfinement phase transition as shown in Fig.\[Tmu1\]. From this figure, one can see that the 