A Case of Well-Defined Thermal Derivative Expansion to Lowest Order

We examine a very simple model for which the leading contribution to the one-loop effective potential at finite temperature is uniquely defined despite the presence of the Landau terms. In addition we report on the usual non-analyticity at finite temperature in order to compare our perturbative results with exact ones obtained in the literature. Finally, we point out the significance of our conclusions in the context of symmetry restoration at finite temperature.