Correlations in vector-spin-glass models in a transverse field

Several publications dealing with the infinite-range quantum XY and Heisenberg spin glasses in an external magnetic field K in the z direction share a common supposition: the correlation between the x and y components of the spins is zero. Using the Matsubara imaginary-time formalism we show that this assumption holds only for those models where K=0. With the help of the Trotter-Suzuki formulation we investigate the phase diagram of the XY model for spin S=1/2, and find that it is different from those previously reported because of the nonzero xy correlation. It is also argued that for a general spin S in the XY model at zero temperature the spin-glass phase persists up to ${\mathit{K}}_{\mathit{c}}$=2S.