We study, in a $d$-dimensional space-time, the nonanalyticity of the thermal free energy in the scalar ${\varphi }^4$ 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.

• Received 20 August 2012

DOI:https://doi.org/10.1103/PhysRevD.86.107701