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QCD at a finite quark-number chemical potential $\mu$ has a complex fermiondeterminant, which precludes its study by standard lattice QCD simulations. Wetherefore simulate lattice QCD at finite $\mu$ in the phase-quenchedapproximation, replacing the fermion determinant with its magnitude. Thesesimulations are used to study the finite temperature transition for small$\mu$,where the position and nature of this transition are expected to beunchanged by this approximation. We look for the expected critical endpoint for3-flavour QCD. Here, it had been argued that the critical point at zero $\mu$would become the critical endpoint at small $\mu$, for quark masses just abovethe critical mass. Our simulations indicate that this does not happen, andthere is no such critical endpoint for small $\mu$. We discuss how we mightadapt techniques used for imaginary $\mu$ to improve the signal/noise ratio andstrengthen our conclusions, using results from relatively low statisticsstudies.

Lattice QCD at finite temperature and density in the phase-quenched approximation