Ising anti-ferromagnets on Husimi trees and the re-entrant phase for three-dimensional lattices

We report here the results of approximating Ising spin systems, with nearest-neighbor anti-ferromagnetic interactions, on the square, simple cubic and body-centered cubic lattices. Our approximations are based on Ising spins on Husimi trees. The critical curves in the magnetic field-temperature plane are discussed with particular emphasis on the possibility of a re-entrant phase being present. In addition we have gathered a rather complete collection of previous results against which we compare our results.