Variational Study of the Phase Transition at Finite T in the $λ φ^4 $-Theory

Details Variational Study of the Phase Transition at Finite T in the $λ φ^4 $-Theory Variational Study of the Phase Transition at Finite T in the $λ φ^4 $-Theory

1995-06-12

arxiv.org/abs/hep-lat/9506019v1

Nucl.Phys.Proc.Suppl. 47 (1996) 713-716

Physics

High Energy Physics

High Energy Physics - Lattice

8 pages, latex, 4 figures available from author e-mail: gpalma@lauca.usach.cl, submitted to Phys. Lett. B

Scientific paper

10.1016/0920-5632(96)00157-0

Assuming triviality of the 4-dimensional $\lambda \phi ^4$-theory we compute the effective potential by means of a self consistent Feynman-Bogoliubov method. This potential $U_{eff}^{FB}$ depends on a UV-cutoff, which is fixed by a stability condition for the gap-equation for the plasma mass. It shows a second order phase transition at zero temperature, in agreement with a large amount of analytical and RG analysis as well as Monte Carlo numerical evidence. As the cutoff $\Lambda $ is removed the renormalized self coupling constant $\lambda _R$ goes to zero consistent with the claim of triviality. At finite temperature the phase transition becomes weakly first order.

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