On the behaviour of the temperature dependent coupling constants

We study the temperature dependence of the coupling constant for the massive lambdaphi4 model. Using the Dyson-Schwinger equations at finite temperature we obtain the behaviour of the coupling constant in the high temperature limit. We compare our results with the ones from the one-loop approximation and the renormalized group method and conclude that, due to the breakdown of the naive perturbation theory at high temperatures, we must improve the evaluation of the β function of the renormalization group in this limit. (orig.)