  We show that the Almeida-Thouless line in Ising spin glasses vanishes when
their dimension d -> 6 as h_{AT}^2/T_c^2 = C(d-6)^4(1- T/T_c)^{d/2 - 1}, where
C is a constant of order unity. An equivalent result which could be checked by
simulations is given for the one-dimensional Ising spin glass with long-range
interactions. It is shown that replica symmetry breaking also stops as d -> 6.
