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

The renormalized zero-momentum four-point coupling gr 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 gr∗ are explicitly computed. Strong-coupling series for lattice non-linear σ models are analyzed near criticality in d = 2 and d = 3 for several values of N and the corresponding values of 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 2d gives the best determination of gr∗ to date (for N = 2,3 it is comparable with the best Monte Carlo estimates); in 3d it is consistent with available φ4 field theory results.