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Philosophical Magazine B

Random site-bond diluted system in the Ising model

Zhen‐Ya Li, Chuan‐Zhang Yang

Published Dec 1, 1985• 2 citations
Publisher

Abstract

In this paper, a random site-bond diluted Ising system on the square lattice is studied by the use of annealed model solutions of the corresponding decoration problem. The critical temperature and magnetization as functions of site and bond concentrations are calculated.
DOI
10.1080/13642818508238958

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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 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.
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.
The hypothesis of weak universality is tested for the moments of the zero-field correlation function and the magnetic-field derivatives of the free energy of dilute Ising models. The investigation, which is carried out for dilution of both the magnetic sites (site dilution) and interactions (bond dilution), is performed just above the critical temperature. In the case of bond dilution both the quenched and annealed distributions are considered. The quenched model is investigated by series methods for site and bond dilution on the face-centred cubic lattice and for bond dilution on the triangular lattice.