  One dimensional spin-1/2 $XXZ$ model in a transverse magnetic field is
studied. It is shown that the field induces the gap in the spectrum of the
model with easy-plain anisotropy. Using conformal invariance the field
dependence of the gap at small fields is found. The ground state phase diagram
is obtained. It contains four phases with different types of the long range
order (LRO) and a disordered one. These phases are separated by critical lines,
where the gap and the long range order vanish. Using scaling estimations and a
mean-field approach as well as numerical calculations in the vicinity of all
critical lines we found the critical exponents of the gap and the LRO. It is
shown that transition line between the ordered and disordered phases belongs to
the universality class of the transverse Ising model.
