Gap generation in the XXZ model in a transverse magnetic field

The ground-state phase diagram of the one-dimensional $\mathrm{XXZ}$ model in a transverse magnetic field is obtained. It consists of the gapped phases with different types of long-range order (LRO) and critical lines at which the gap and the LRO vanish. Using scaling estimations and a mean-field approach as well as numerical results we found critical indices of the gap and the LRO in the vicinity of critical lines.