One dimensional spin-1/2 $XXZ$ model in a transverse magnetic field isstudied. It is shown that the field induces the gap in the spectrum of themodel with easy-plain anisotropy. Using conformal invariance the fielddependence of the gap at small fields is found. The ground state phase diagramis obtained. It contains four phases with different types of the long rangeorder (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 amean-field approach as well as numerical calculations in the vicinity of allcritical lines we found the critical exponents of the gap and the LRO. It isshown that transition line between the ordered and disordered phases belongs tothe universality class of the transverse Ising model.
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