Construction of a non-trivial planar field theory with ultraviolet stable fixed point

We study a ₄ ⁴ planar euclidean quantum field theory with propagator 1/p ^2–/2,>0. With the help of the tree expansion of Gallavotti and Nicolò 1], this non-renormalizable theory is shown to have a non-trivial ultraviolet-stable fixed point at negative coupling constant. The vicinity of the fixed point is discussed.