MAGNETIC PHASE-DIAGRAM OF THE S=1 AXIAL NEXT-NEAREST-NEIGHBOR ISING (ANNNI) MODEL WITH HIGHER-ORDER SPIN INTERACTION

The three-dimensional S = 1 axial next-nearest-neighbour Ising (ANNNI) model is discussed. In addition to the ferromagnetic intra- and inter layer interactions J0 and J1 two types of competing antiferromagnetic interactions are considered between next-nearest layers, i.e. ordinary two-site two-spin J2S(i)S(i+2) ([2-2] model) or three-site four-spin J3S(i)S(i+1)2S(i+2) ([3-4] model) interactions. For both models, the m agnetic phase diagrams are obtained by means of the site-dependent mol ecular field approximation. The phase boundaries among paramagnetic, f erromagnetic and various modulated phases are determined by analysing frequency-dependent susceptibility chi(q), or by solving coupled equat ions of [S(i)] and [S(i)2] for spins up to 17, iteratively. The constr ucted 'devil's flower' of the [3-4] model is characteristically differ ent from that of the [2-2] model, since three-site four-spin interacti on is effectively temperature-dependent. For the [3-4] model, a new be haviour of re-entrant transition is found for the interaction ratio -0 .50 > J3/J1 > -0.53. The role of the entropy term for this re-entrant transition is discussed in detail by analysing the free energies aroun d the multiphase point (T = 0, J3/J1 = -0.5).