Two phenomenological models describing an $\mathrm{SU}\left(N\right)\mathrm{}$ 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 $N=2\mathrm{}$ deconfinement transition is second order in both models, while $N=3,\hspace{0.5em}4,$ and $5$ are first order. Both models appear to have a smooth large-N limit. For $N>~4,$ 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 $1$ is responsible for the approach to the blackbody limit over the range $T_d-{5T}_d.$ The addition of massless quarks in $\mathrm{SU}\left(3\right)\mathrm{}$ breaks $Z\left(3\right)\mathrm{}$ symmetry weakly and eliminates the deconfining phase transition. In contrast, a first-order phase transition persists with sufficiently heavy quarks.

• Received 2 August 2001

DOI:https://doi.org/10.1103/PhysRevD.65.034009