First and second order phase transitions in gauge theories at finite temperature

We consider in general the nature of the phase transition which occurs in 4D gauge theories coupled to scalar and spinor fields at finite temperature. It is shown that the critical behavior can be isolated in an effective 3D theory of the zero frequency mode whose lagrangian may be calculated explicitly in weak coupling perturbation theory. This lagrangian, in turn, may be investigated by means of standard ?-expansion techniques. Theories with an asymptotically free gauge coupling constant possess no stable fixed point in the ?-expansion and are inferred to have weakly first-order phase transitions; theories not satisfying this condition may have second-order transitions.