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

M. Campostrini·A. Pelissetto·P. Rossi·E. Vicari
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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 $β$-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 $ϕ^4$ field theory results.

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M. Campostrini, A. Pelissetto, P. Rossi, E. Vicari. 1995-06-01. Four-point renormalized coupling constant in O(N) models. https://doi.org/10.1016/0550-3213(95)00569-2

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