Given some restriction on the interaction parameters, the critical temperature for the spin-one Ising model on a honeycomb lattice described with the Blume-Emery-Griffiths Hamiltonian with random non-magnetic impurities in equilibrium (annealed site-disorder case) is obtained exactly.
A new decoration method is presented which allows the quenched randomly diluted site-bond spin-1 Ising model on a regular lattice along a line in the plane of exchange interaction parameters versus temperature to be mapped onto a certain class of mixed-spin decorated-lattice problem. Approximate results for the quenched, randomly diluted site-bond, spin-1 Ising model on the honeycomb lattice are obtained through the use of the exact solution of the annealed model on the corresponding decorated lattice. The critical temperature and the magnetisation of the diluted system as functions of site and bond concentrations are calculated in detail.
The spin-1 Ising model with bilinear (J) and biquadratic (K) nearest-neighbor exchange interactions and a single-ion potential (\ensuremath{\Delta}), a model introduced by Blume, Emery, and Griffiths (BEG), is studied on a honeycomb lattice. The exact solution of the BEG model is obtained for a certain relation K=K(J). Also an approximate treatment of the BEG model outside the surface, in the space of coupling constants, given by the relation above is discussed. Finally a digression is made on the critical temperature of the spin-1 Ising model.
The Ising model on the honeycomb lattice with spins of magnitudes 1/2 and s with random exchange constant and random uniaxial anisotropy is considered. The two cases are studied separately, and in both cases binary annealed distributions of the random parameters are considered. An exact solution is obtained by mapping the model onto the uniform spin 1/2 Ising model on the triangular lattice, and the transition temperature is determined as a function of the parameters for arbitrary s. Explicit results are presented for s=1 and s=3/2, and it is shown that some critical parameters, surprisingly, are not universal.