Transverse Ising antiferromagnetic in a longitudinal magnetic field: study of the ground state

The two-dimensional antiferromagnetic Ising model in a transverse magnetic field (Ω) and uniform longitudinal field is studied for the first time (H). Using the effective-field theory (EFT) with correlation in one-site cluster calculation the ground-state phase diagram in the Ω-H plane is determined for the honeycomb (z=3) and square (z=4) lattices. It is shown that there is an order-disordered transition line (second-order phase transition) qualitatively in agreement with rigorous results of renormalization group in d=1. The critical curve in the classical approach is also obtained and the results are compared