$1/N$ Expansion of Two-Dimensional Models in the Scaling Region

Details $1/N$ Expansion of Two-Dimensional Models in the Scaling Region $1/N$ Expansion of Two-Dimensional Models in the Scaling Region

1992-10-08

arxiv.org/abs/hep-lat/9210011v1

Nucl. Phys. Proc. Suppl. 30 (1993) 827

Physics

High Energy Physics

High Energy Physics - Lattice

6 pages, report no. IFUP-TH 49/92

Scientific paper

10.1016/0920-5632(93)90335-4

The main technical and conceptual features of the lattice $1/N$ expansion in the scaling region are discussed in the context of a two-parameter two-dimensional spin model interpolating between $CP^{N-1}$ and $O(2N)$ $\sigma$ models, with standard and improved lattice actions. We show how to perform the asymptotic expansion of effective propagators for small values of the mass gap and how to employ this result in the evaluation of physical quantities in the scaling regime. The lattice renormalization group $\beta$ function is constructed explicitly and exactly to $O({1/N})$.

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