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

Abstract

The magnetization process of the Ising model with first- and second-neighbour interactions, J1 and J2 respectively, was studied for all combinations of signs and magnitudes of J1 and J2 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 j1>0, -1/2< gamma < infinity , then F. (ii) When J1<0, J2>0, then AF to P. (iii) When J1<0, 0< gamma <1/2, then AF to IV to AF to P. (iv) When J1<0, 1/2< gamma < infinity , then SAF to IV to P. (v) When J1>0, - infinity < gamma <-1/2, then SAF to P, where gamma =z2J2/z1J1, and z1 and z2 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 J2/J1.