$\delta$-Expansion at Finite Temperature

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 within this perturbative approach the renormalized mass at finite temperature at a finite order in $\delta$. The results are compared with the usual loop-expansion at finite temperature.