Phenomenological equations of state for the quark-gluon plasma

Two phenomenological models describing an (Formula presented) 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 (Formula presented) and has the correct blackbody behavior for large temperatures. The (Formula presented) deconfinement transition is second order in both models, while (Formula presented) and (Formula presented) are first order. Both models appear to have a smooth large-N limit. For (Formula presented) it is shown that the trace of the Polyakov loop is insufficient to characterize the phase structure; the free energy is best described using the eigenvalues of the Polyakov loop. 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 (Formula presented) is responsible for the approach to the blackbody limit over the range (Formula presented) The addition of massless quarks in (Formula presented) breaks (Formula presented) symmetry weakly and eliminates the deconfining phase transition. In contrast, a first-order phase transition persists with sufficiently heavy quarks.