Non-Trivial Phase Structure of $φ^{4}$-Theory at Finite Temperature

Details Non-Trivial Phase Structure of $φ^{4}$-Theory at Finite Temperature Non-Trivial Phase Structure of $φ^{4}$-Theory at Finite Temperature

1993-05-04

arxiv.org/abs/hep-ph/9305209v1

Phys.Lett. B311 (1993) 207-212

Physics

High Energy Physics

High Energy Physics - Phenomenology

10 LaTex pages (2 figures available on request), UNITUE-THEP-5-1993

Scientific paper

10.1016/0370-2693(93)90556-W

The effective potential for the local composite operator $\phi^{2}(x)$ in $\lambda \phi^{4}$-theory is investigated at finite temperature in an approach based on path-integral linearisation of the $\phi^4 $-interaction. At zero temperature, the perturbative vacuum is unstable, because a non-trivial phase with a scalar condensate $\langle \phi ^{2} \rangle _{0}$ has lower effective action. Due to field renormalisation, $\langle \lambda \phi ^{2} \rangle _{0}$ is renormalisation group invariant and leads to the correct scale anomaly. At a critical temperature $T_{c}$ the non-perturbative phase becomes meta-stable implying a first order phase-transition to the perturbative phase. The ratio $\langle\lambda \phi^{2} \rangle _{0} / T_{c}^{2} \approx 62$ turns out to be a universal constant.

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