Renormalization group flow of two-dimensional hierarchical Heisenberg model of Dyson-Wilson type

Two-dimensionalO(N)-invariant hierarchical Heisenberg models (of Dyson-Wilson type) are investigated by the real space renormalization group method. It is established that ifN2, then the effective actions at long distance scales are driven into the high temperature region by the iterative use of the block spin transformations thus concluding the non-existence of phase transitions in the system. The correlation functions are also obtained and they decay at the speed of massive gaussian field model. The driving force is geometrical and an a priori one and stronger than the boundary effect which is bounded byO(1) in the present system. Thus the hierarchical formulas fail to exhibit the Kosterlitz-Thouless transitions (at least forN=2).