ON THE RENORMALIZATION-GROUP ITERATION OF A 2-DIMENSIONAL HIERARCHICAL NONLINEAR O (N) SIGMA-MODEL

We investigate the behaviour of a simplified two-dimensional non-linear O(N)sigma-model under Wilson renormalization group transformations in the small coupling region. It can be controlled rigorously by suitable bounds on polymer activities uniformly for all field configurations, i.e. there is no need for a separate discussion of large and small field domains. This investigation provides us some preliminary insights to the renormalization group flow of and to phase space expansion methods applied to the complete sigma-model.