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.
Categories: hep-ph cond-mat