Canonical partition function and finite density phase transition in lattice QCD

We discuss the nature of the phase transition for lattice QCD at finite temperature and density. We propose a method to calculate the canonical partition function by fixing the total quark number introducing approximations allowed in the low density region. An effective potential as a function of the quark number density is discussed from the canonical partition function. We analyze data obtained in a simulation of two-flavor QCD using p4-improved staggered quarks with bare quark mass m/T=0.4 on a 16(3)x4 lattice. The results suggest that the finite density phase transition at low temperature is of first order.