Trajectories of the PHI44-model by the block spin transformations

Trajectories of the O(N)-invariant PHI44-models (N=1 or infinite) by the iterations of the block spin transformations are obtained by using the hierarchical approximation due to Gawedzki and Kupiainen. The correlation functions are also obtained. In the case of N=infinite, it is shown that the theory does not exist below the critical temperature and there exists only one fixed point. This fixed point turns out to be trivial (Gaussian). For N=1, the correlation functions and the trajectories are also obtained in the high and at the critical temperature. They are more or less equivalent to those of the O(infinite) model. (orig.)