$delta$-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.