Existence of the critical point in finite density lattice QCD

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 greater than or similar to 2.5. We also discuss the difference between the phase structures of QCD with nonzero quark chemical potential and nonzero isospin chemical potential.