Study of the critical point in lattice QCD at high temperature and density

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 $m\mathrm{/}T=0.4$, and find that a first order phase transition line appears in the high density regime for ${\mu }_q\mathrm{/}T\sim 2.5$. 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.