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We consider the position of the deconfining critical endpoint, where thefirst order transition for deconfinement is washed out by the presence ofmassive, dynamical quarks. We use an effective matrix model, employedpreviously to analyze the transition in the pure glue theory. If the param-eters of the pure glue theory are unaffected by the presence of dynamicalquarks, and if the quarks only contribute perturbatively, then for three colorsand three degenerate quark flavors this quark mass is very heavy, m_de \sim 2.5GeV, while the critical temperature, T_de, barely changes, \sim 1% below thatin the pure glue theory. The location of the deconfining critical endpoint is asensitive test to differentiate between effective models. For example, modelswith a logarithmic potential for the Polyakov loop give much smaller values ofthe quark mass, m_de \sim 1 GeV, and a large shift in T_de \sim 10% lower thanthat in the pure glue theory.

Critical endpoint for deconfinement in matrix and other effective models