Magnetization process and the critical field of the Ising model with first- and second-neighbour interactions

The magnetization process of the Ising model with first- and second-neighbour interactions, J 1 and J 2 respectively, was studied for all combinations of signs and magnitudes of J 1 and J 2 by the four-sublattice molecular-field approximation. For the square and BCC lattices, ferro- (F) or paramagnetic phase (P), antiferromagnetic phase (AF), superantiferromagnetic phase (SAF) and type IV phase (IV) appear and the transitions among them are classified as: (i) When j 1 >0, - 1 / 2 < gamma < infinity , then F. (ii) When J 1 <0, J 2 >0, then AF to P. (iii) When J 1 <0, 0< gamma < 1 / 2 , then AF to IV to AF to P. (iv) When J 1 <0, 1 / 2 < gamma < infinity , then SAF to IV to P. (v) When J 1 >0, - infinity < gamma <- 1 / 2 , then SAF to P, where gamma =z 2 J 2 /z 1 J 1 , and z 1 and z 2 are the numbers of the first- and second-neighbour interactions. The critical field, the magnetization curve, and the location of the critical point and the tricritical point were calculated for typical values of J 2 /J 1 .