Quantum Potts gauge-matter systems at finite temperature

A systematic large-N expansion for gauge-matter Potts systems at finite temperature is presented. This allows us to explore the interior of the phase diagrams, taking into account all terms in the hamiltonian. Calculations are carried out in 3 + 1 and 2 + 1 dimensions and the expansion parameter is 1/Nsup(1/d), where d is the number of space dimensions. For singly charged matter the Higgs-confinement phase is analytically connected to a high-temperature plasma phase. When the matter fields are multiply charged, both Higgs and confinement phases undergo a finite-temperature phase transition. The free charge phase may or may not undergo a phase transition depending on the number of space-time dimensions. Implications for other models, both abelian and non-abelian are discussed. We also comment on applications to quantum spin systems. (orig.)