Confinement Models at Finite Temperature and Density

In-medium chiral symmetry breaking in confining potential models of QCD is examined. Past attempts to analyse these models have been hampered by infrared divergences that appear at non-zero temperature. We argue that previous attempts to circumvent this problem are not satisfactory and demonstrate a simple resolution. We also show that the expectation that confining models do not exhibit a chiral phase transition is incorrect. The effect of summing ring diagrams is investigated and we present the first determination of the temperature-density phase diagram for two model systems. We find that observables and the phase structure of the confinement models depend strongly on whether quark polarisation is accounted for. Finally, it appears that standard confinement models cannot adequately describe both hadron phenomenology and in-medium properties of QCD.