The strong coupling limit (βgauge=0) of lattice QCD with staggered fermions enjoys the same non-perturbative properties as continuum QCD, namely confinement and chiral symmetry breaking. In contrast to the situation at weak coupling, the sign problem which appears at finite density can be brought under control for a determination of the full (μ,T) phase diagram by Monte Carlo simulations. Further difficulties with efficiency and ergodicity of the simulations, especially at the strongly first-order, low-T, finite-μ transition, are addressed respectively with a worm algorithm and multicanonical sampling. Our simulations reveal sizeable corrections to the old results of Karsch and Mütter. Comparison with analytic mean-field determinations of the phase diagram shows discrepancies of O(10) in the location of the QCD critical point.

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