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

The two-dimensional antiferromagnetic Ising model in a transverse magnetic field (Omega) 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 Omega-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. (C) 2004 Published by Elsevier B.V.