Renormalization-group-invariant 1/N corrections to nontrival φ⁴ theory

In the framework of path integral linearization techniques, the effective potential and the master field equation for massless φ⁴ theory, in the modified loop expansion around the mean field, are derived up to next to leading order. In the O(N)-symmetric theory, these equations are equivalent to a subsummation of O(N) and order 1 diagrams. A renormalization prescription is proposed which is manifestly renormalization group invariant. The numerical results for the potential in next to leading order agree qualitatively well with the leading order ones. In particular, the nontrivial phase structure remains unchanged. Quantitatively, the corrections ar small for N≫8, but even for N as small as one their essential effect is to modify the scaling coefficient β₀ in the Callan-Symanzik β function, in accordance with conventional loop expansions. The numerical results are best parametrized by scaling improved mean field formulas. Dimensional transmutation renders the overall (physical) mass scale M₀, generated by a dynamical breaking of scale invariance, the only adjustable parameter of the theory. Renormalization group invariance of the numerical results is explicitly verified.