Lattice Perturbation Theory for $O(N)$-Symmetric $σ$-Models with General Nearest-Neighbour Action I. Conventional Perturbation Theory

Details Lattice Perturbation Theory for $O(N)$-Symmetric $σ$-Models with General Nearest-Neighbour Action I. Conventional Perturbation Theory Lattice Perturbation Theory for $O(N)$-Symmetric $σ$-Models with General Nearest-Neighbour Action I. Conventional Perturbation Theory

1994-01-15

arxiv.org/abs/hep-lat/9401015v1

Nucl.Phys. B420 (1994) 141-183

Physics

High Energy Physics

High Energy Physics - Lattice

42 pages, 4 postscript figures included at the end of the file

Scientific paper

10.1016/0550-3213(94)90378-6

We compute the beta-function and the anomalous dimension of all the non-derivative operators of the theory up to three-loops for the most general nearest-neighbour O(N)-invariant action together with some contributions to the four-loop beta-function. These results are used to compute the first analytic corrections to various long-distance quantities as the correlation length and the general spin-$n$ susceptibility. It is found that these corrections are extremely large for $RP^{N-1}$ models (especially for small values of N), so that asymptotic scaling can be observed in these models only at very large values of beta. We also give the first three terms in the asymptotic expansion of the vector and tensor energies.

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