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physica status solidi (b)

A theoretical study of the thermodynamic properties of diluted and random‐bond ising systems

Ana Cecilia Agudelo, O. E. Ospina, Ligia Edith Zamora, Alberto Bohorquez, German Antonio Pérez Alcázar

Published Jun 1, 1994• 0 citations
Publisher

Abstract

Abstract The thermodynamic properties of a diluted and random‐bond Ising model are calculated using the variational method based on the Bogolyubov's inequality for the ferro‐ and antiferromagnetic regions. It is assumed that the system is composed of clusters of one and two spins. Previously reported results for Ising models pure and diluted by site and by bond are recovered with this model.

DOI
10.1002/pssb.2221830221

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Abstract The thermodynamic properties of a diluted and random‐bond Ising model are calculated using the variational method based on the Bogolyubov's inequality for the ferro‐ and antiferromagnetic regions. It is assumed that the system is composed of clusters of one and two spins. Previously reported results for Ising models pure and diluted by site and by bond are recovered with this model.
Abstract The thermodynamical properties of the site‐ and bond‐diluted transverse Ising model with anisotropic coupling constants are studied by using a variational procedure based on Bogolyubov's inequality. Within this approach the thermal behaviour of the system is obtained in the entire range of temperature (0 ≤ T < ∞). The results for the critical temperature, critical transverse field, and critical concentration are, in several cases, comparable to the constant‐coupling approximation.
We have performed Monte Carlo calculations of the thermodynamic properties of the bond-dilute Ising model on the square lattice. The results are obtained for the magnetization, internal energy, specific heat, and susceptibility for several concentrations of missing bonds. The dependence of the Curie temperature on dilution is in good agreement with the results obtained by other methods. The phase transition is found to remain sharp with the same value of the susceptibility exponent as for the pure Ising model.
Magnetic properties of the annealed quenched systems each in the bond and site models are investigated by the Kikuchi pair approximation. In the annealed system, phase diagrams and susceptibilities are obtained. Two critical temperatures in some case in the bond system and no critical concentration in the site system are obtained. The physical interpretation of them is given. In the quenched system, two different approximate conditions are considered for the complete randomness. The case of the first condition is equivalent to the cluster variation method proposed by Sato, Arrott and Kikuchi, and the results are in agreement with those obtained by Katsura and Matsubara. The second is essentially equivalent to the average coordination number method by Sato, Arrott and Kikuchi for the dilute ferromagnetism. However, the results for both cases are unreliable at low temperatures, because of the appearance of negative entropy. This is inevitable under the pair condition.