Critical temperatures of classicaln-vector models on hypercubic lattices

The critical temperature Tc(n,d) of a classical n-component spin model on a d-dimensional hypercubic lattice is expanded in powers of 1/d to fifth order. In the spherical-model limit, n→∞, the expansion is derived exactly to all orders and shown rigorously to be only asymptotic, although Tc(∞,d) is analytic in d for 2<d<∞.