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

Abstract

The effective potential for the local composite operator ${\varphi }^2(x)$ in $\lambda {\varphi }^4$-theory is investigated at finite temperature in an approach based on path-integral linearisation of the ${\varphi }^4$-interaction. At zero temperature, the perturbative vacuum is unstable, because a non-trivial phase with a scalar condensate $⟨{\varphi }^2{⟩}_0$ has lower effective action. Due to field renormalisation, $⟨\lambda {\varphi }^2{⟩}_0$ 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 $⟨\lambda {\varphi }^2{⟩}_0/T_c^2\approx 62$ turns out to be a universal constant.

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