Two-Loop Effective Potential of λø24 Without Cut-Off Dependence

The effective potential of λø⁴ theory in two-dimensional spacetime is calculated up to twoloop level in an operator approach (or causd approach) without divergence. It reveals a second-order phase transition. A further discussion about the rdation between the convexity of the full effective potential and phase transition is given. We propose a modified Feynman path integral (FPI) representation of λø₂⁴ and sketch a plausible proof for the convexity of its full effective potential.