  We propose a new algorithm to solve the quasi-Wigner solution of the gap
equation beyond chiral limit. Employing a Gaussian gluon model and rainbow
truncation, we find that the quasi-Wigner solution exists in a limited region
of current quark mass, $m<43.1$ MeV, at zero temperature $T$ and zero chemical
potential $\mu$. The difference between Cornwall-Jackiw-Tomboulis (CJT)
effective actions of quasi-Wigner and Nambu-Goldstone solutions shows that the
Nambu-Goldstone solution is chosen by physics. Moreover, the quasi-Wigner
solution is studied at finite temperature and chemical potential, the far
infrared mass function of quasi-Wigner solution is negative and decrease along
with $T$ at $\mu=0$. Its susceptibility is divergent at certain temperature
with small $m$, and this temperature decreases along with $m$. Taking $T=80$
MeV as an example, the quasi-Wigner solution is shown at finite chemical
potential upto $\mu=350$ MeV as well as Nambu solution, the coexistence of
these two solutions indicates that the QCD system suffers the first order phase
transition. The first order chiral phase transition line is determined by the
difference of CJT effective actions.
