Non-trivial phase structure of φ4-theory at finite temperature

Abstract

The effective potential for the local composite operator φ 2( x) in λφ 4-theory is investigated at finite temperature in an approach based on path-integral linearisation of the φ 4-interaction. At zero temperature, the perturbative vacuum is unstable, because a non-trivial phase with a scalar condensate 〈 φ 2〉 0 has lower effective action. Due to field renormalisation, 〈 λφ 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 〈 λφ 2〉 0/ T c 2 ≈ 62 turns out to be a universal constant.