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

Abstract

We study the behavior of two diferent models at finite temperature in a $D$-dimensional spacetime. The first one is the $\lambda {\phi }^4$ model and the second one is the Gross-Neveu model. Using the one-loop approximation we show that in the $\lambda {\phi }^4$ 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 $(\lambda {\phi }^4{)}_{D=3}$ model there is a temperature ${\beta }_{\star }^{-1}$ 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 $D\ne 3$ our results are inconclusive. Pacs numbers: 11.10.Ef, 11.10.Gh

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Cited by in corpus (7)

• Spontaneous Symmetry Breaking in Compactified $\lambda {\varphi }^4$ Theory
• Boundary dependence of the coupling constant and the mass in the vector N-component $(\lambda {\varphi }^4{)}_D$ theory
• Finite Size Effects in the Anisotropic λ/4!(ϕ^4_1 + ϕ^4_2)_d Model
• The thermal coupling constant and the gap equation in the $\lambda {\varphi }_D^4$ model
• The Distributional Zeta-Function in Disordered Field Theory
• Analytic regularization of the Yukawa Model at Finite Temperature
• Finite-Size Effects in Disordered $\lambda {\varphi }^4$ Model