Absence of re-entrant phase transition of the antiferromagnetic Ising   model on the simple cubic lattice: Monte Carlo study of the hard-sphere   lattice gas
  We perform the Monte Carlo simulations of the hard-sphere lattice gas on the simple cubic lattice with nearest neighbour exclusion. The critical activity is estimated, $z_{\rm c} = 1.0588 \pm 0.0003$. Using a relation between the hard-sphere lattice gas and the antiferromagnetic Ising model in an external magnetic field, we conclude that there is no re-entrant phase transition of the latter on the simple cubic lattice. 
Atsushi Yamagata