Critical parameters of N-vector spin models on 3d lattices from high temperature series extended to order β21

High temperature expansions for the free energy, the susceptibility and the second correlation moment of the classical N-vector model [also denoted as the O(N) symmetric classical spin Heisenberg model or as the lattice O(N) nonlinear sigma model] have been extended to order β21 on the simple cubic and the body centered cubic lattices, for arbitrary N. The series for the second field derivative of the susceptibility has been extended to order β17. An analysis of the newly computed series yields updated estimates of the model's critical parameters in good agreement with present renormalization group estimates. (orig.)