On the finite temperature $λφ^{4}$ and Gross-Neveu models. Is there a first order phase transition in $(λφ^{4})_{D=3}$?

We study the behavior of two diferent models at finite temperature in a $D$-dimensional spacetime. The first one is the $λφ^{4}$ model and the second one is the Gross-Neveu model. Using the one-loop approximation we show that in the $λφ^{4}$ 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 $(λφ^{4})_{D=3}$ model there is a temperature $β^{-1}_{\star}$ 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

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