de Almeida-Thouless line in vector spin glasses

We consider the infinite-range spin glass in which the spins have m > 1 components (a vector spin glass). Applying a magnetic field which is random in direction, there is a de Almeida-Thouless (AT) line below which the replica symmetric solution is unstable, just as for the Ising (m=1) case. We calculate the location of this AT line for Gaussian random fields for arbitrary m and verify our results by numerical simulations for m=3.