Reduced Transfer Matrix Approach for Ising Model

Kaya, Tuncer; Arik, Murat

doi:10.1142/s0217979211101235

Cited by 6 publications

(2 citation statements)

References 33 publications

(8 reference statements)

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“…In this section, we are going to use the reduced transfer matrix method previously introduced [12,13]. In order to improve the accuracy of estimation of critical coupling strength.…”

Section: Reduced Transfer Matrix Methodsmentioning

confidence: 99%

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Configurational mean-field reduced transfer matrix method for Ising systems

Kaya

Tambaş

2020

Mod. Phys. Lett. B

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A mean-field method for the hypercubic nearest-neighbor Ising system is introduced and applications to the method are demonstrated. The main idea of this work is to combine the Kadanoff’s mean-field approach with the model presented by one of us previously. The mean-field approximation is introduced with the replacement of the central spin in Ising Hamiltonian with an average value of particular spin configuration, i.e, the approximation is taken into account within each configuration. This approximation is used in two different mean-field-type approaches. The first consideration is a pure-mean-field-type treatment in which all the neighboring spins are replaced with the assumed configurational average. The second consideration is introduced by the reduced transfer matrix method. The estimations of critical coupling values of the systems are evaluated both numerically and also analytically by the using of saddle point approximation. The analytic estimation of critical values in the first and second considerations are [Formula: see text] and [Formula: see text] respectively. Obviously, both of the considerations have some significant deviation from the exact treatment. In this work, we conclude that the method introduced here is more appropriate physical picture than self-consistent mean-field-type models, because the method introduced here does not presume the presence of the phase transition from the outset. Consequently, the introduced approach potentially makes our research very valuable mean-field-type picture for phase transition treatment.

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“…In this section, we are going to use the reduced transfer matrix method previously introduced [12,13]. In order to improve the accuracy of estimation of critical coupling strength.…”

Section: Reduced Transfer Matrix Methodsmentioning

confidence: 99%

“…In addition, estimations of critical coupling strengths of mean-field-type theories are fairly good when they are compared with the series or exact predictions. Therefore, a further improvement of the mean-field-type theory is still important and many attempts have been made in recent years [8][9][10][11][12][13].…”

Section: Introductionmentioning

confidence: 99%

Configurational mean-field reduced transfer matrix method for Ising systems

Kaya

Tambaş

2020

Mod. Phys. Lett. B

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Exact three spin correlation function relations for the square and the honeycomb Ising lattices

Kaya

2020

Chinese Journal of Physics

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Correlated Reduced Transfer Matrix Approach for Ising Model

Kaya

2012

Int. J. Mod. Phys. B

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In this paper we present a simple approximate transfer matrix method for 2D and 3D hyper cubic nearest neighbor Ising models with various coordination number z to calculate the corresponding critical coupling strengths Kc. The critical coupling strengths of the Ising ferromagnets are obtained quite accurately by simple improvements over the self-consistent correlated field (SCCF) approximation. The important physical effect included in this work is some of the fluctuation effects of the systems by the help of a reduced transfer matrix method. When used in combination with the accuracy of the average magnetization obtained from the SCCF approximation, this reduced transfer matrix method leads to estimate of Kc more accurate than those obtained from the Bethe–Peierls–Weiss approximation and also SCCF approximation. Therefore, we believe that the approach we refer to as the correlated reduced transfer matrix method is potentially very useful scheme for obtaining approximate values of the critical coupling strengths of the Ising models with a mathematically easy meaner.

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Reduced Transfer Matrix Approach for Ising Model

Cited by 6 publications

References 33 publications

Configurational mean-field reduced transfer matrix method for Ising systems

Configurational mean-field reduced transfer matrix method for Ising systems

Exact three spin correlation function relations for the square and the honeycomb Ising lattices

Correlated Reduced Transfer Matrix Approach for Ising Model

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