We study the behavior of two diferent models at finite temperature in a $D$-dimensional spacetime. The first one is the $\lambda\varphi^{ 4}$ model and the second one is the Gross-Neveu model. Using the one-loop approximation we show that in the $\lambda\varphi^{ 4}$ model the thermal mass increase with the temperature while the thermal coupling constant decrese with the temperature. Using this facts we establish that in the $(\lambda\varphi^{ 4})_{ D=3}$ model there is a temperature $\beta^{ -1}_{ \star}$ above which the system can develop a first order phase transition, where the origin corresponds to a metastable vacuum. In the massless Gross-Neveu model, we demonstrate that for $D=3$ the thermal correction to the coupling constant is zero. For $D\neq 3$ our results are inconclusive. Pacs numbers: 11.10.Ef, 11.10.Gh
Categories: hep-th