Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Progress of Theoretical Physics

Random Mixtures in Annealed and Quenched Ising Bond Model

Andrzej Pękalski, T. Oguchi

Published Oct 1, 1975• 14 citations
Publisher

Abstract

The two-dimensional Ising model with two kinds of bonds –ferro and antiferromagnetic– is investigated in both quenched and annealed approximations. High temperature series expansion technique is used to get the respective free energies and susceptibilities. Form the analysis of the ratio method results, the phase diagrams are drawn and critical concentrations are estimated. It is shown that in both approximations the system behaves similarly, although in the annealed case the magnetically ordered phases are more stable against increasing impurity concentration. It is also proved that for Bethe lattices initial susceptibilities for quenced and annealed systems coincide.

DOI
10.1143/ptp.54.1021

Related papers

Critical temperature of mixed ferromagnetic and antiferromagnetic Ising systems with arbitrary spin

J Jakubczak, Z. Mrozińska, Andrzej Pękalski

Using the high-temperature series expansion method, a system of randomly mixed ferromagnetic and antiferromagnetic Ising bonds is considered in quenched and annealed systems for an arbitrary value of spin and a BCC lattice. The dependence of the critical temperature on the concentration p of ferromagnetic bonds is determined. It is found that the resulting phase diagrams depend on the system (whether quenched or annealed), the spin value and the strength of the coupling constants. Also the dependence of the critical exponent gamma on p and the crossover exponent phi are estimated.

Journal of Physics C Solid State Physics•Jun 28, 1979•5 citations

Theory of Random Mixtures of Ising Spins

Yohtaro Ueno, T. Oguchi

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.

Progress of Theoretical Physics•Sep 1, 1975•17 citations

Concentration Expansion for Random Ising Systems

Tsuguhiro Tamaribuchi, F. Takano

Two-dimensional Ising systems with bond-impurities are treated exactly by using the method of Gibberd and Hurst. First we derive recurrence equations by which a Green's function with n scattering centers can be obtained from that with n-1 scattering centers. Using these recurrence equations, we are able to expand the free energy systematically in power series of concentration c of impure bonds. This concentration expansion is carried out up to the order of c2 for quenched and annealed systems, and we discuss critical properties of the quenched system comparing with those of the annealed system. The difference between the two systems is seen to arise first in the term of the order c2, but the singularities in these terms are almost the same for both systems. This result leads to an conjecture that critical properties of a quenched system are the same as those of an annealed system in the critical region. The shift of the critical temperature in the quenched system is also calculated up to the order of c2 in the bond-dilution case (the strength of the impurity bonds is zero).

Progress of Theoretical Physics•Oct 1, 1980•11 citations

High Temperature Series Expansion of the Susceptibility of the d-Dimensional Random Ising Model

Shigeru Okamoto, T. Oguchi, Yohtaro Ueno

The critical temperatures of the random mixtures are investigated in the quenched site and bond Ising model with the ferromagnetic and antiferromagnetic exchange interactions by the high-temperature series expansion of the susceptibility for the d-dimensional simple hypercubical lattices. (d = 2, 3, 4, 5, 6)

Progress of Theoretical Physics•Feb 1, 1982•2 citations

Statistical Theory of the Random Ordered Phase in Quenched Bond Mixtures

Takehiko Oguchi, Yohtaro Ueno

Statistical theory based on generalized Bethe approximation is developed for the Ising quenched bond model in which ferromagnetic and antiferromagnetic exchange integrals exist. The random ordered phase (ROP) proposed in a previous paper is obtained. The random susceptibility χ r is calculated, and it is found that χ r diverges at the critical temperature T c . It is pointed out that the ordinary susceptibility for the uniform field might have a cusp at T c .

Journal of the Physical Society of Japan•Oct 1, 1976•19 citations

Concentration Expansion for Random Ising Systems. II

Tsuguhiro Tamaribuchi

A new method for the concentration expansion of the free energy of the two-dimensional Ising system with binary bond mixture is given. This method is simpler and more systematic compared with that used in a previous paper by the author and Takano. By using this new method, the expansion is carried out up to the order of c3, where c is the concentration of impurity bonds. The result is shown to be consistent with the assumption on functional form of the internal energy proposed in the previous paper. This assumption leads us to a conclusion that the specific heat anomaly in the quenched system is a cusp as in the annealed system.

Progress of Theoretical Physics•Nov 1, 1981•6 citations
The two-dimensional Ising model with two kinds of bonds –ferro and antiferromagnetic– is investigated in both quenched and annealed approximations. High temperature series expansion technique is used to get the respective free energies and susceptibilities. Form the analysis of the ratio method results, the phase diagrams are drawn and critical concentrations are estimated. It is shown that in both approximations the system behaves similarly, although in the annealed case the magnetically ordered phases are more stable against increasing impurity concentration. It is also proved that for Bethe lattices initial susceptibilities for quenced and annealed systems coincide.
Using the high-temperature series expansion method, a system of randomly mixed ferromagnetic and antiferromagnetic Ising bonds is considered in quenched and annealed systems for an arbitrary value of spin and a BCC lattice. The dependence of the critical temperature on the concentration p of ferromagnetic bonds is determined. It is found that the resulting phase diagrams depend on the system (whether quenched or annealed), the spin value and the strength of the coupling constants. Also the dependence of the critical exponent gamma on p and the crossover exponent phi are estimated.
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.
Two-dimensional Ising systems with bond-impurities are treated exactly by using the method of Gibberd and Hurst. First we derive recurrence equations by which a Green's function with n scattering centers can be obtained from that with n-1 scattering centers. Using these recurrence equations, we are able to expand the free energy systematically in power series of concentration c of impure bonds. This concentration expansion is carried out up to the order of c2 for quenched and annealed systems, and we discuss critical properties of the quenched system comparing with those of the annealed system. The difference between the two systems is seen to arise first in the term of the order c2, but the singularities in these terms are almost the same for both systems. This result leads to an conjecture that critical properties of a quenched system are the same as those of an annealed system in the critical region. The shift of the critical temperature in the quenched system is also calculated up to the order of c2 in the bond-dilution case (the strength of the impurity bonds is zero).
A new method for the concentration expansion of the free energy of the two-dimensional Ising system with binary bond mixture is given. This method is simpler and more systematic compared with that used in a previous paper by the author and Takano. By using this new method, the expansion is carried out up to the order of c3, where c is the concentration of impurity bonds. The result is shown to be consistent with the assumption on functional form of the internal energy proposed in the previous paper. This assumption leads us to a conclusion that the specific heat anomaly in the quenched system is a cusp as in the annealed system.