Ising Spin System of S = 1 on a Triangular Lattice with Three‐Site Four‐Spin Interaction

For the Ising ferromagnet of S = 1 on the triangular lattice, the effects of the three‐site four‐spin interaction J ′( S i · S j ) ( S j · S k ) on the magnetization S z is studied by the use of the four‐spin model approximation. The ferromagnetic order established by the ferromagnetic bilinear exchange interaction J and by the three‐site four‐spin interaction J ′ are destroyed by the three‐site four‐spin interaction at the condition of J ′ = − J /16 and by the antiferromagnetic bilinear exchange interaction at the condition of J = −6 J ′, respectively. Furthermore, the ground state spin structures and the condition for an occurrence of the phase transition are determined from the behavior of the J ′‐dependence of the energy for a single spin in various spin structures.