Phase diagrams of the transverse Ising antiferromagnet in the presence of the longitudinal magnetic field

In this paper we study the critical behavior of the two-dimensional antiferromagnetic Ising model in both uniform longitudinal ( H ) and transverse ( Ω ) magnetic fields. Using the effective-field theory (EFT) with correlation in single site clusters we calculate the phase diagrams in the H − T and Ω − T planes for the square lattice. We have only found second order phase transitions for all values of fields and reentrant behavior was not observed.