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 ($\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 $\Omega -T$ 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. 
Minos A. Neto, J. Ricardo de Sousa
cond-mat.stat-mech