The critical points of lattice QCD with a non--zero quark density
  We study the interplay of quark number density and chiral symmetry in lattice QCD. We suggest that both are controlled by the eigenvalue spectrum of the fermionic propagator matrix, which shapes the pattern of zeros of the partition function. The onset of the quark current would be triggered by the lowest lying eigenvalue, the chiral transition by the density of zeros, the two critical points being distinct in full QCD, and coincident in the quenched approximation. Our preliminary estimate for the critical point in full QCD in the infinite couling limit compares favourably with the predictions of the strong coupling expansions and of numerical simulations based on exact, alternative representations of the partition function. Several reasons of perplexity however remain, which are briefly discussed. 
M.-P. Lombardo