  We propose a method to probe the nature of phase transitions in lattice QCD
at finite temperature and density, which is based on the investigation of an
effective potential as a function of the average plaquette. We analyze data
obtained in a simulation of two-flavor QCD using p4-improved staggered quarks
with bare quark mass $m/T = 0.4$, and find that a first order phase transition
line appears in the high density regime for $\mu_q/T \sim 2.5$. The effective
potential as a function of the quark number density is also studied. We
calculate the chemical potential as a function of the density from the
canonical partition function and discuss the existence of the first order phase
transition line.
