Abstract
A high-temperature series for the spin-glass order-parameter susceptibility is presented for n-component spins on a d-dimensional hypercubic lattice. The coupling between neighbouring spins is taken to be a Gaussian random variable. The series is analysed for the cases of XY(n=2) and Heisenberg (n=3) spins. In each case the transition temperature falls to zero near four dimensions, indicating that there is no Edwards-Anderson order in less than four dimensions.