On the spontaneous ordering of the mixed-spin Ising square lattice with singly and triply decorated bonds

Abstract

The mixed-spin Ising model on a square lattice with singly and triply decorated bonds is exactly solved within the framework of the decoration–iteration transformation, which establishes a precise mapping relationship between the investigated model system and the equivalent spin-1/2 Ising model on an anisotropic square (rectangular) lattice. The effect of uniaxial single-ion anisotropy, which acts on the decorating spin-1 atoms, is examined in particular. It is shown that the investigated model displays a very peculiar critical behaviour as a result of the single-ion anisotropy strengthening because it remains spontaneously long range ordered despite its quasi-1D character in a certain range of single-ion anisotropies before it enters the disordered phase. The single-ion anisotropy parameter is also responsible for diverse temperature dependences of sublattice and total magnetization.