How Wide is the Transition to Deconfinement?

Pure SU(3) glue theories exhibit a deconfining phase transition at a nonzero temperature, Tc. Using lattice measurements of the pressure, we develop a simple matrix model to describe the transition region, when T > Tc. This model, which involves three parameters, is used to compute the behavior of the 't Hooft loop. There is a Higgs phase in this region, where off diagonal color modes are heavy, and diagonal modes are light. Lattice measurements of the latter suggests that the transition region is narrow, extending only to about 1.2 Tc. This is in stark contrast to lattice measurements of the renormalized Polyakov loop, which indicates a much wider width. The possible implications for the differences in heavy ion collisions between RHIC and the LHC are discussed.