The Coleman-Weinberg Mechanism and First Order Phase Transitions

We study the Coleman-Weinberg phenomenon in a U(N)×U(N) symmetric scalar model in 4 dimensions. By comparing the numerical simulation results with the bare perturbation calculation in the weak bare coupling region, we demonstrate explicitly that a first order transition is induced by loop-effects. We also observed first order phase transitions in the strong coupling region. Email address: [email protected] It is well known that a system with more than one relevant coupling can have a first order phase transition induced by quantum loop fluctuations – a phenomenon first discovered by Coleman and Weinberg [1, 2, 3]. The application of this Coleman-Weinberg mechanism led to a lower bound of 7-10 GeV on the Higgs mass in the Standard Model [4, 5] and to the suggestion that the QCD finite temperature chiral restoration phase transition might be first order for more than two quark flavor[6]. It has also been suggested that the ColemanWeinberg mechanism might be relevant for chiral symmetry breaking in technicolor models [7]. Recently [8] it was pointed out that the Coleman-Weinberg mechanism might be used to place constraints on the top condensate model or strong-coupling extended technicolor models. Let us consider the action (in Euclidean form)