Nonanalyticity of the free energy in thermal field theory
F. T. Brandt, J. Frenkel, J. B. Siqueira
TL;DR
This paper investigates the nonanalytic behavior of the thermal free energy in scalar phi^4 theory and QED across different dimensions, revealing dimension-dependent nonanalyticities caused by infrared divergences.
Contribution
It provides a detailed analysis of how infrared divergences induce nonanalyticities in the free energy depending on the space-time dimension.
Findings
Nonanalyticity in even dimensions scales as (alpha)^[(d-1)/2]
In odd dimensions, nonanalyticity appears as a logarithmic term
Infrared divergences are responsible for these nonanalytic behaviors
Abstract
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.
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