Phenomenological Models of the Quark-Gluon Plasma Equation of State

Two phenomenological models describing an SU(N) quark-gluon plasma are presented. The first is obtained from high temperature expansions of the free energy of a massive gluon, while the second is derived by demanding color neutrality over a certain length scale. Each model has a single free parameter, exhibits behavior similar to lattice simulations over the range T_d-5T_d, and has the correct blackbody behavior for large temperatures. The N=2 deconfinement transition is second order in both models, while N=3,4, and 5 are first order. Both modelsappear to have a smooth large-N limit. In both models, the confined phase is characterized by a mutual repulsion of Polyakov loop eigenvalues that makes the Polyakov loop expectation value zero. In the deconfined phase, the rotation of the eigenvalues in the complex plane towards 1 is responsible for the approach to the blackbody limit over the range T_d-5T_d. The addition of quarks in SU(3) breaks Z(3) symmetry weakly and eliminates the deconfining phase transition for sufficiently light quarks.