Non-linear solutions of the renormalization group equations in the large-n limit

The renormalization group equations of Ma (1974) for the n-vector model in the limit of large n are solved exactly. The solutions are given in terms of the non-linear scaling fields of Wegner (1972), both in the trivial fixed-point representation and the non-trivial fixed-point representation. The effective exponent for the susceptibility crossover is computed and it is shown that the semi-microscopic theory of Riedel and Wegner (1974) is contained in the present theory as a lowest-order approximation in the most relevant scaling field.