Exact Beta Functions in the Vector Model and Renormalization Group Approach

Details Exact Beta Functions in the Vector Model and Renormalization Group Approach Exact Beta Functions in the Vector Model and Renormalization Group Approach

1993-03-16

arxiv.org/abs/hep-th/9303090v2

Phys.Lett. B312 (1993) 88-96

Physics

High Energy Physics

High Energy Physics - Theory

13 pages (no figures) in LaTeX, TIT/HEP-215, NUP-A-93-4, a few minor corrections

Scientific paper

10.1016/0370-2693(93)90493-2

The validity of the renormalization group approach for large $N$ is clarified by using the vector model as an example. An exact difference equation is obtained which relates free energies for neighboring values of $N$. The reparametrization freedom in field space provides infinitely many identities which reduce the infinite dimensional coupling constant space to that of finite dimensions. The effective beta functions give exact values for the fixed points and the susceptibility exponents.

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