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We discuss the nature of the phase transition for lattice QCD at finitetemperature and density. We propose a method to calculate the canonicalpartition function by fixing the total quark number introducing approximationsallowed in the low density region. An effective potential as a function of thequark number density is discussed from the canonical partition function. Weanalyze data obtained in a simulation of two-flavor QCD using p4-improvedstaggered quarks with bare quark mass $m/T = 0.4$ on a $16^3 \times 4$ lattice.The results suggest that the finite density phase transition at low temperatureis of first order.

Canonical partition function and finite density phase transition in lattice QCD