Journal of Statistical Physics, Vol. 115, Nos. 5/6, June 2004. p. 1669-1713.
The renormalization group transformation for the hierarchical O(N)spin model in four dimensions is studied by means of characteristic functions of single-site measures, and convergence of the critical trajectory to the Gaussian fixed point is shown for a sufficiently large N. In the strong coupling regime, the trajectory is controlled by the help of the exactly solved O(infinity) trajectory, while, in the weak coupling regime, convergence to the Gaussian fixed point is shown by power decay of the effective coupling constant.