Faria da Veiga P.A., O'Carroll M., Schor R.
A Classical Large $N$ Hierarchical Vector Model in Three
Dimensions: A Nonzero Fixed Point and Canonical Decay of Correlation
Functions
(63K, LATeX 2e)
ABSTRACT. We consider a hierarchical $N$-component classical vector model
on a
three-dimensional lattice ${\Z}^3$ for large $N$. The model differs from
the usual one in that the kernel of the inverse Laplace operator is
non-translational invariant but has matrix elements which are positive and
exhibit the same falloff as the inverse Laplacian in ${\Z}^3$. We
introduce a renormalization group transformation and for $N=\infty$,
corresponding to the leading order of the $1/N$ expansion, we construct
explicitly a nonzero fixed point for this transformation and also obtain
some correlation functions. The two-point function has canonical
decay. For $1\ll N<\infty$, we obtain the fixed point and
the two-point function in the first $1/N$ approximation. Canonical decay is
still obtained, in contrast to what is reported for the full model.