Anisotropic Heisenberg chain in coexisting transverse and longitudinal magnetic fields

The one-dimensional spin-1/2 $XXZ$ model in a mixed transverse and longitudinal magnetic field is studied. Using the specially developed version of the mean-field approximation the order-disorder transition induced by the magnetic field is investigated. The ground state phase diagram is obtained. The behavior of the model in low transverse field is studied on the base of conformal field theory. The relevance of our results to the observed phase transition in the quasi-one-dimensional antiferromagnet $Cs_2 Co Cl_4$ is discussed.