Four-point renormalized coupling constant in O(N) models

Details Four-point renormalized coupling constant in O(N) models Four-point renormalized coupling constant in O(N) models

1995-09-05

arxiv.org/abs/hep-lat/9509005v1

Nucl.Phys.Proc.Suppl. 47 (1996) 751-754

Physics

High Energy Physics

High Energy Physics - Lattice

4 pages, to be published in the Proceedings of Lattice 95, Postscript file

Scientific paper

10.1016/0920-5632(96)00166-1

The renormalized zero-momentum four-point coupling $g_r$ of $O(N)$-invariant scalar field theories in $d$ dimensions is studied by applying the $1/N$ expansion and strong coupling analysis. The $O(1/N)$ correction to the $\beta$-function and to the fixed point value $g_r^*$ are explictly computed. Strong coupling series for lattice non-linear $\sigma$ models are analyzed near criticality in $d=2$ and $d=3$ for several values of $N$ and the corresponding values of $g_r^*$ are extracted. Large-$N$ and strong coupling results are compared with each other, finding a good general agreement. For small $N$ the strong coupling analysis in 2-d gives the best determination of $g^*_r$ to date (or comparable for $N=2,3$ with the available Monte Carlo estimates), and in 3-d it is consistent with available $\phi^4$ field theory results.

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