 98249 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)
Apr 1, 98

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Abstract. We consider a hierarchical $N$component classical vector model
on a
threedimensional lattice ${\Z}^3$ for large $N$. The model differs from
the usual one in that the kernel of the inverse Laplace operator is
nontranslational 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 twopoint function has canonical
decay. For $1\ll N<\infty$, we obtain the fixed point and
the twopoint function in the first $1/N$ approximation. Canonical decay is
still obtained, in contrast to what is reported for the full model.
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