On the 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 $\mu_q/T \simge 2.5$. We also discuss the difference between the phase structures of QCD with non-zero quark chemical potential and non-zero isospin chemical potential.