Phenomenological Equations of State for SU(N) Gauge Theories

Two phenomenological models describing an SU(N) gluon plasma are presented using the eigenvalues of the Polyakov loop as the order parameters of the deconfinement transition. Each model has a single free parameter and exhibits behavior similar to lattice simulations over the range T_d-5T_d. The N=2 deconfinement transition is second order in both models, while N=3,4, and 5 are first order. Both models appear to have a smooth large-N limit. The confined phase is characterized by a mutual repulsion of Polyakov loop eigenvalues that makes the Polyakov loop expectation value zero. The motion of the eigenvalues is responsible for the approach to the blackbody limit over the range T_d-5T_d.