Solution to the 3-loop $\Phi$-derivable Approximation for Scalar Thermodynamics

Abstract

We solve the 3-loop $\Phi$-derivable approximation to the thermodynamics of the massless ${\varphi }^4$ field theory by reducing it to a 1-parameter variational problem. The thermodynamic potential is expanded in powers of $g^2$ and $m/T$, where $g$ is the coupling constant, $m$ is a variational mass parameter, and $T$ is the temperature. There are ultraviolet divergences beginning at 6th order in $g$ that cannot be removed by renormalization. However the finite thermodynamic potential obtained by truncating after terms of 5th order in $g$ and $m/T$ defines a stable approximation to the thermodynamic functions.

4 pages, 1 figure

References in corpus (1)

• Mass Expansions of Screened Perturbation Theory

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