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

Abstract

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 ${\lambda }_1=J_y/J_x({\lambda }_2=J_z/J_x)=1$ (anisotropic sc). Our results indicate second-order frontiers for all values of $H$ for the particular case ${\lambda }_2=0$ (square lattice), while in case ${\lambda }_1={\lambda }_2=1$, 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.