  We consider the D3-D7 model and use the spectral function of a probe fermion
on D7 to analyze the first order phase transition from the black-hole embedding
phase to another black-hole embedding phase in the presence of the finite
density and temperature. From the fermionic spectral functions, we study the
temperature dependence of the decay rate, and we observe various phenomena that
support the first order phase transition including jump in it at the critical
temperature that corresponds to the first order phase transition.
