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Critical endpoint for deconfinement in matrix and other effective models

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