Nonanalyticity of the free energy in thermal field theory

We study, in a d-dimensional space-time, the nonanalyticity of the thermal free energy in the scalar phi^4 theory as well as in QED. We find that the infrared divergent contributions induce, when d is even, a nonanalyticity in the coupling alpha of the form (alpha)^[(d-1)/2] whereas when d is odd the nonanalyticity is only logarithmic.