98-249 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 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.

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