Confinement models at finite temperature and density

This work presents a non-perturbative study of dynamical chiral symmetry breaking in various confinement models at finite temperature and density. The tool of choice is the Schwinger-Dyson equations. We shall discuss (i) the inadequacy of static confinement models in explaining thermal properties of QCD (ii) dynamical chiral and parity symmetry breaking of three dimensional QED with two-component fermions (iii) endemic infrared divergences in QED3 at finite temperature and the attempt to solve the system self-consistently.