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

Abstract

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 $g_r^{\ast }$ 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 $g_r^{\ast }$ 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 $g_r^{\ast }$ to date (or comparable for $N=2,3$ with the available Monte Carlo estimates), and in 3-d it is consistent with available ${\varphi }^4$ field theory results.

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

References in corpus (2)

• Critical exponents for 3D O(n)-symmetric model with n > 3
• Scaling behavior of the four-point renormalized coupling constant in the two dimensional O(2) and O(3) non-linear sigma models

Cited by in corpus (2)

• Comparison of the O(3) Bootstrap $\sigma$-Model with the Lattice Regularization at Low Energies
• Does the XY Model have an integrable continuum limit?