Non-perturbative Evaluation of the Effective Potential of λφ⁴ Theory at Finite Temperature under the Super-Daisy Approximation

We calculate the effective potential of the scalar theory at finite temperature under the super-daisy approximation, after expressing its derivative with respect to mass square in terms of the full propagator. This expression becomes the self-consistent equation for the derivative of the effective potential. We find the phase transition is first order with this approximation. We compare our result with others.