  The ground state phase diagram of the alternating spin-1/2 chains with
anisotropic ferromagnetic coupling under the influence of a symmetry breaking
transverse magnetic field is studied. We have used the exact diagonalization
technique. In the limit where the antiferromagnetic coupling is dominant, we
have identified two Ising-type quantum phase transitions. We have calculated
two critical fields $h_{c_{1}}$ and
  $h_{c_{2}}$, corresponding to the transition between different magnetic
phases of the system. It is found that the intermediate state
($h_{c_{1}}<h<h_{c_{2}}$) is gapful, describing the stripe-antiferromagnetic
phase.
