The Chiral Critical Surface of QCD

We calculate the critical surface bounding the region featuring chiral phase transitions in the quark mass and chemical potential parameter space of QCD with three flavours of quarks. Our calculations are valid for small to moderate quark chemical potentials, mu less than or similar to T. In a first step, we compute the leading Taylor coefficients of an expansion in mu/T for the theory with three degenerate flavours in two different ways and demonstrate, that such an expansion is controllable. Next we extend our calculations to the case of non-degenerate quark masses. These calculations are done on coarse N-t = 4 lattices. Finally, we present first results for the N-f = 3 QCD phase diagram at zero and finite density on N-t = 6 lattices, corresponding to a lattice spacing of a similar to 0.2 fm.