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 ($\mathrm{\Omega }$) magnetic fields. Using the effective-field theory (EFT) with correlation in single site cluster we calculate the phase diagrams in the $H-T$ and $\mathrm{\Omega }-T$ planes for the square ($z=4$) lattices. We have only found second order phase transitions for all values of fields and reentrant behavior was not observed.