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Journal of Physics Condensed Matter

The randomly diluted site-bond, spin-1 Ising model on a honeycomb lattice

Zhenlin Wang, Zhen‐Ya Li

Published Oct 29, 1990• 5 citations
Publisher

Abstract

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.

DOI
10.1088/0953-8984/2/43/007

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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.
A new decoration method is proposed which can achieve an exact mapping between the quenched bond randomly diluted spin-1 Ising model on a regular lattice in the subspace: exp(K)cosh (J) =1 and a certain class of mixed-spin quenched site randomly diluted decorated-lattice problem. Using this mapping in conjunction with the annealed model solution for the decorated-lattice problem, we have obtained the approximate results for the quenched bond randomly diluted spin-1 Ising model on the honeycomb lattice. The critical temperature and the magnetization of the diluted system as functions of bond concentration are calculated in detail.
A general technique is presented which allows site-bond disorder problems in Ising systems to be mapped onto a certain class of decorated lattice problems. The specific case of site-bond disorder on the honeycomb lattice is studied in detail through the use of annealed model solutions of the corresponding decoration problems. The critical temperature and magnetisation as functions of bond and site concentrations are calculated. The zero-temperature magnetisation is used to obtain an approximation to the percolocation probability of the system.
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.
A systematic cluster extension of the effective-interaction approximation for quenched-bond disorder in random Ising systems is proposed. For bond dilution, exact results for the critical concentrations are obtained in the single-bond approximation for the self-dual square lattice and in the three-bonds approximation for the dual triangular and honeycomb lattices. Qualitative changes in the critical line are observed in the frustration model when going from the single-bond to the three-bonds approximations.