Effective Potential at Finite Temperature: RG improvement vs. High temperature expansion

We have applied the recently proposed renormalization group improvement procedure of the finite temperature effective potential, and have investigated extensively the phase structure of the massive scalar $\phi^4$ model, showing that the $\phi^4$ model has a rich 3-phase structure at $T \neq 0$, two of them are not seen in the ordinary perturbative analysis. Temperature dependent phase transition in this model is shown to be strongly the first order.