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The Ising antiferromagnet on an anisotropic simple cubic lattice in the presence of a magnetic field

We have studied the anisotropic three-dimensional nearest-neighbor Ising model with competitive interactions in an uniform longitudinal magnetic field $H$. The model consists of ferromagnetic interaction $J_{x}(J_{z})$ in the $x(z)$ direction and antiferromagnetic interaction $J_{y}$ in the $y$ direction. We have compared our calculations within a effective-field theory in clusters with four spins (EFT-4) in the simple cubic (sc) lattice with traditional Monte Carlo (MC) simulations. The phase diagrams in the $h-k_{B}T/J_{x}$ plane ($h=H/J_{x}$) were obtained for the particular case $λ_{1}=J_{y}/J_{x} (λ_{2}=J_{z}/J_{x})=1$ (anisotropic sc). Our results indicate second-order frontiers for all values of $H$ for the particular case $λ_{2}=0$ (square lattice), while in case $λ_{1}=λ_{2}=1$, we observe first- and second-order phase transitions in the low and high temperature limits, respectively, with presence of a tricritical point. Using EFT-4, a reentrant behavior at low temperature was observed in contrast with results of MC.