1N-expanded ϕ2X model. I. Phase transition

We consider the ?²X model in a $\text{1}\text{N}$ expansion in six-dimensional Euclidean spacetime. Using the path-integral formalism and the method of stationary phase we show the existence of two phases in the model: with broken O(N) symmetry and with O(N) maintained. In both phases the massless ? fields acquire masses. -Expressions for the masses including $\text{1}\text{N}$ order are given.