  The classical transverse field Ising spin- glass model with short-range
interactions is investigated beyond the mean- field approximation for a real d-
dimensional lattice. We use an appropriate nontrivial modification of the
Bethe- Peierls method recently formulated for the Ising spin- glass. The zero-
temperature critical value of the transverse field and the linear
susceptibility in the paramagnetic phase are obtained analytically as functions
of dimensionality d. The phase diagram is also calculated numerically for
different values of d. In the limit d -> infinity, known mean- field results
are consistently reproduced.
