Critical Temperature for the $\LAMBDA (\PHI^{4})_{4}$ Theory within the $\DELTA$ -Expansion

Abstract

We apply the $\delta$-expansion perturbation scheme to the $\lambda \phi_{4}$ self-interacting scalar field theory in 3+1 D at finite temperature. In the $\delta$-expansion the interaction term is written as $\lambda (\phi^{2})^{1 + \delta}$ and $\delta$ is considered as the perturbation parameter. We compute, in this perturbation approach, the renormalized mass at finite temperature from which we get the critical temperature. The results are compared with the usual loop-expansion at finite temperature.