RENORMALIZED COUPLINGS AND SCALING CORRECTION AMPLITUDES IN THE N-VECTOR SPIN MODELS ON THE SC AND THE BCC LATTICES

For the classical N-vector model, with arbitrary N, we have computed t hrough order beta(17) the high-temperature expansions of the second he ld derivative of the susceptibility chi(4)(N, beta) on the simple cubi t and on the body centered cubic lattices. [The N-vector model is also known as the O(N) symmetric classical spin Heisenberg model or, in qu antum field theory, as the lattice O(N) nonlinear sigma model.] By ana lyzing the expansion of chi(4)(N, beta) on the two lattices, and by ca refully allowing for the corrections to scaling, we obtain updated est imates of the critical parameters and more accurate tests of the hyper scaling relation dv(N) + gamma(N) - 2 Delta(4)(N) = 0 for a range of v alues of the spin dimensionality N, including N = 0 (the self-avoiding walk model), N = 1 (the Ising spin 1/2 model), N = 2 (the XY model), N = 3 (the classical Heisenberg model). Using the recently extended se ries for the susceptibility and for the second correlation moment, we also compute the dimensionless renormalized Four point coupling consta nts and some universal ratios of scaling correction amplitudes in fair agreement with recent renormalization group estimates. [S0163-1829(98 )04941-8].