  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.
