Hiroshi WATANABE
Triviality of hierarchical O(N) spin model in four dimensions with large N
(86K, LaTeX2e)

ABSTRACT.  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(\infty) trajectory, while, in the weak coupling 
regime, convergence to the Gaussian fixed point is shown by power decay of the effective 
coupling constant.