  We study the ground state phase diagram of a two-leg spin ladder with
anisotropic ferromagnetic leg couplings under the influence of a symmetry
breaking transverse magnetic field by the exact diagonalization technique. In
the case of antiferromagnetic coupling between legs we identified two phase
transitions in the plane of magnetic field vs interchain coupling strength. The
first one corresponds to the transition from the gapped rung-singlet phase to
the gapped stripe-ferromagnetic phase. The second one represents the transition
from the gapped stripe-ferromagnetic phase into the fully polarized
ferromagnetic phase.
