A CLASSICAL LARGE N-HIERARCHICAL VECTOR MODEL IN 3 DIMENSIONS - A NONZERO FIXED-POINT AND CANONICAL DECAY OF CORRELATION-FUNCTIONS

We consider a hierarchical N-component classical vector model on a thr ee-dimensional lattice Z(3), for large N. The model differs from the u sual one in that the kernel of the inverse Laplace operator is nontran slational invariant but has matrix elements which are positive and exh ibit the same falloff as the inverse Laplacian in Z(3). We introduce a renormalization group transformation and for N=infinity, correspondin g to the leading order of the 1/N expansion, we construct explicitly a nonzero fixed point for this transformation and also obtain some corr elation functions. The two-point function has canonical decay. For 1 m uch less than N<asymptotic to, we Obtain the fixed point and the two-p oint function in the first 1/N approximation. Canonical decay is still verified, in contrast to what is reported for the full model. (C) 199 8 American Institute of Physics.