On the finite temperature λ 4 model. Is there a first order phase transition in (λ 4)3?

We investigate the behavior at finite temperature of the massive λ 4 model in a D-dimensional space time, performing a renormalization up to the order of one loop. In this approximation we show that the thermal mass increases with the temperature, while the thermal coupling constant decreases with the temperature. We establish that in the (λ 4)3 model there is a temperature β*−1 above which the coupling constant becomes negative. We argue that the system could develop a first-order-phase transition, where the origin corresponds to a metastable vacuum.