physica status solidi (b)

Mean Field Renormalization Group for Site‐Bond Diluted Ising Ferromagnets

C. Z. Yang, Z. Y. Li

Published Mar 1, 1988• 12 citations

Abstract

Abstract It is shown that the mean field renormalization group techniques provide a reasonable description of the critical behaviour of the site‐bond diluted Ising model, both in the two‐dimensional system and the surface of a semi‐infinite three‐dimensional system.

DOI: 10.1002/pssb.2221460123

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Critical properties of site-diluted Heisenberg and Ising magnets

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Mean-field renormalization group: Approach to the diluted site-bond-correlated Ising model

J. Ricardo de Sousa, Douglas F. de Albuquerque

Physical review. B, Condensed matterDec 1, 19938 citations

Phase diagrams of the diluted and random-bond Ising model

Ligia Edith Zamora, German Antonio Pérez Alcázar, Alberto Bohorquez +2 more

The quenched-bond disordered Ising model is studied by means of the mean-field renormalization-group approach. Besides dilution and ferromagnetic random bond, the probability distribution function also includes two extra competing random bonds which can be ferromagnetic or antiferromagnetic, depending on the sign of some competing parameters. The critical temperature against ferromagnetic bond concentration phase diagrams are analyzed for several values of the theoretical parameters.

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physica status solidi (b)

Mean Field Renormalization Group for Site‐Bond Diluted Ising Ferromagnets

C. Z. Yang, Z. Y. Li

Published Mar 1, 1988• 12 citations

Publisher

Abstract

DOI: 10.1002/pssb.2221460123

Related papers

Mean field renormalisation group for the disordered transverse Ising model

J. A. Plascak

Journal of Physics A Mathematical and GeneralApr 1, 198424 citations

Critical properties of the site-diluted Ising ferromagnet

Julia M. Yeomans, Robin B. Stinchcombe

Journal of Physics C Solid State PhysicsJul 14, 197828 citations

STUDY OF SURFACE MAGNETISM IN A SEMI-INFINITE ISING FERROMAGNETIC SYSTEM

JIANG QIN, Zhenya Li, 苏州大学物理系

Acta Physica SinicaJan 1, 19891 citation

Critical properties of site-diluted Heisenberg and Ising magnets

Andrzej Komoda, Andrzej Pękalski

A simple modification of the real-space renormalisation group method is used to discuss critical behaviour of site diluted spin- 1 / 2 Ising and Heisenberg ferromagnets in two and three dimensions. The critical parameters and critical exponents are evaluated, and are shown to be in good agreement with the exact results and series calculations for site-diluted Ising ferromagnets on the square and triangular lattices. Good values of the critical parameters have also been obtained for the site-diluted Heisenberg and Ising models in two and three dimensions using the Migdal-Kadanoff approximation (1976).A simple modification of the real-space renormalisation group method is used to discuss critical behaviour of site diluted spin- 1 / 2 Ising and Heisenberg ferromagnets in two and three dimensions. The critical parameters and critical exponents are evaluated, and are shown to be in good agreement with the exact results and series calculations for site-diluted Ising ferromagnets on the square and triangular lattices. Good values of the critical parameters have also been obtained for the site-diluted Heisenberg and Ising models in two and three dimensions using the Migdal-Kadanoff approximation (1976).

Journal of Physics C Solid State PhysicsJun 10, 19836 citations

Mean-field renormalization group: Approach to the diluted site-bond-correlated Ising model

J. Ricardo de Sousa, Douglas F. de Albuquerque

We study the diluted site-bond-correlated (SBC) Ising model within the scheme of the mean-field renormalization group. The SBC Ising model has been proposed to describe the phase diagram for ${\mathrm{KNi}}_{\mathit{p}}$ ${\mathrm{Mg}}_{1\mathrm{\ensuremath{-}}\mathit{p}}$ ${\mathrm{F}}_{3}$ . One treats the square (Z=4) and simple cubic (Z=6) lattices by using two different exchange interactions (denoted by models A and B). In the present paper, the phase diagram for some values of the correlation parameter \ensuremath{\alpha}, which range from zero to unity, is studied. We obtain two critical concentrations ${\mathit{p}}_{\mathit{c}}$ (\ensuremath{\alpha}=0) and ${\mathit{p}}_{\mathit{c}}$ (\ensuremath{\alpha}\ensuremath{\ne}0) in agreement with results from Monte Carlo methods. In addition, an interesting universal relation between the initial slope ${\mathrm{\ensuremath{\Delta}}}^{(\mathrm{\ensuremath{\mu}})}$(\ensuremath{\alpha}=1) and ${\mathrm{\ensuremath{\Delta}}}^{(\mathrm{\ensuremath{\mu}})}$(\ensuremath{\alpha}=0) is obtained (\ensuremath{\mu} denotes model A or B). From this relation, we can estimate the possible exact values to the initial slope on the completely correlated case. Our approach is valid for lattices with any coordination number Z.We study the diluted site-bond-correlated (SBC) Ising model within the scheme of the mean-field renormalization group. The SBC Ising model has been proposed to describe the phase diagram for ${\mathrm{KNi}}_{\mathit{p}}$${\mathrm{Mg}}_{1\mathrm{\ensuremath{-}}\mathit{p}}$${\mathrm{F}}_{3}$. One treats the square (Z=4) and simple cubic (Z=6) lattices by using two different exchange interactions (denoted by models A and B). In the present paper, the phase diagram for some values of the correlation parameter \ensuremath{\alpha}, which range from zero to unity, is studied. We obtain two critical concentrations ${\mathit{p}}_{\mathit{c}}$(\ensuremath{\alpha}=0) and ${\mathit{p}}_{\mathit{c}}$(\ensuremath{\alpha}\ensuremath{\ne}0) in agreement with results from Monte Carlo methods. In addition, an interesting universal relation between the initial slope ${\mathrm{\ensuremath{\Delta}}}^{(\mathrm{\ensuremath{\mu}})}$(\ensuremath{\alpha}=1) and ${\mathrm{\ensuremath{\Delta}}}^{(\mathrm{\ensuremath{\mu}})}$(\ensuremath{\alpha}=0) is obtained (\ensuremath{\mu} denotes model A or B). From this relation, we can estimate the possible exact values to the initial slope on the completely correlated case. Our approach is valid for lattices with any coordination number Z.

Physical review. B, Condensed matterDec 1, 19938 citations

Phase diagrams of the diluted and random-bond Ising model

Ligia Edith Zamora, German Antonio Pérez Alcázar, Alberto Bohorquez +2 more

Physical review. B, Condensed matterApr 1, 199523 citations

We study the diluted site-bond-correlated (SBC) Ising model within the scheme of the mean-field renormalization group. The SBC Ising model has been proposed to describe the phase diagram for

{\mathrm{KNi}}_{\mathit{p}}

${\mathrm{Mg}}_{1\mathrm{\ensuremath{-}}\mathit{p}}$

{\mathrm{F}}_{3}

. One treats the square (Z=4) and simple cubic (Z=6) lattices by using two different exchange interactions (denoted by models A and B). In the present paper, the phase diagram for some values of the correlation parameter \ensuremath{\alpha}, which range from zero to unity, is studied. We obtain two critical concentrations

{\mathit{p}}_{\mathit{c}}

(\ensuremath{\alpha}=0) and

{\mathit{p}}_{\mathit{c}}

(\ensuremath{\alpha}\ensuremath{\ne}0) in agreement with results from Monte Carlo methods. In addition, an interesting universal relation between the initial slope ${\mathrm{\ensuremath{\Delta}}}^{(\mathrm{\ensuremath{\mu}})}$(\ensuremath{\alpha}=1) and ${\mathrm{\ensuremath{\Delta}}}^{(\mathrm{\ensuremath{\mu}})}$(\ensuremath{\alpha}=0) is obtained (\ensuremath{\mu} denotes model A or B). From this relation, we can estimate the possible exact values to the initial slope on the completely correlated case. Our approach is valid for lattices with any coordination number Z.