Finite Temperature One-Loop Renormalization of <math>λϕ4</math> and Gross-Neveu Model - The Search for Triviality

Nota de FísicaPublicado

Finite Temperature One-Loop Renormalization of $<math>\lambda\varphi^{4}</math>$ and Gross-Neveu Model - The Search for Triviality

A.P.C. Malbouisson; N.F. Svaiter

1994

Autores: A.P.C. Malbouisson; N.F. Svaiter
Tipo: Nota de Física
Estado: Publicado
Fecha de publicación: 1994
Descripción: We investigate the temperature dependent one-loop effective potential associated with two different models in a generic D dimensional spacetime. The first one is the massive self-interacting <math>\lambda\varphi^{4}\,\!</math> model. The second is the Gross-Neveu model. We analize the possibility of triviality in these models at some temperature and also calculed the <math>{\mathcal B}\,\!</math> coefficient of the Callan-Zymanzik equations in the situations where triviality can be achieved. In the <math>\lambda\varphi^{4}\,\!</math> model for <math>D=4\,\!</math> the renormalized coupling constant attains its maximum at zero temperature and decreases monotonically as the temperature increases, so there is no triviality in this case. The situation is quite different for <math>D<4\,\!</math>, where the renormalized coupling constant vanishes at some finite temperature <math>\beta^{-1}_{T}\,\!</math>. Above this triviality temperature, the effective potential becomes unbounded bellow, corresponding to a metastable vacuum. In the massless Gross-Neveu model for <math>D=3\,\!</math> the thermal contribution to the renormalized coupling constant is zero, which means at least in the one-loop aproximation, triviality cannot be obtained.
Año: 1994
Número: CBPF-NF-044/94
Vínculo con tesis: No
Vínculo con beca: No