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

Journal of Physics Condensed Matter

Position-space renormalization-group investigation of the spin-3/2 Blume-Emery-Griffiths model with repulsive biquadratic coupling

A. Bakchich, M. El Bouziani

Published Dec 6, 2000• 25 citations
Publisher

Abstract

Phase transitions of a four-component lattice gas or spin-3/2 Blume-Emery-Griffiths model, with a single-ion uniaxial anisotropy and nearest-neighbour pair interactions, both bilinear and biquadratic, are investigated for two-dimensional lattices using an approximate renormalization-group approach of the Migdal-Kadanoff type. The set of fixed points and flows provide the characteristic phase diagrams, in the case of repulsive biquadratic interaction, featuring four ordered phases including high-entropy ferrimagnetic and staggered quadrupolar phases. Successive phase transitions and multicritical points are also found.

DOI
10.1088/0953-8984/13/1/309

Related papers

Renormalization-group approach to surface critical behavior in the semi-infinite spin- 32 Blume-Emery-Griffiths model

A. Bakchich, M. El Bouziani

Using a renormalization-group transformation in position space based on the Migdal-Kadanoff recursion relations, we investigate the three-dimensional semi-infinite cubic spin-$\frac{3}{2}$ Blume-Emery-Griffiths model with single-site uniaxial anisotropy and nearest-neighbor pair interactions, both bilinear and biquadratic. The fixed-point topologies and corresponding phase diagrams predicted for this model are presented. Attention is focused on the renormalization-group description of the surface critical behaviors, in comparison with the mean-field approximation results. Three main classes of system phase diagrams are determined, featuring a rich variety of phase transitions associated with the surface with type being according to the values of bulk and surface interaction parameters. Surface critical, tricritical, bicritical, and multicritical points are also found.

Physical review. B, Condensed matter•Jan 19, 2001•17 citations

New Phases and Multiple Re-entrance of the Blume-Emery-Griffiths Model with Repulsive Biquadratic Coupling: Monte Carlo Renormalization-Group Theory

Roland R. Netz

We studied the spin-1 Ising model on cubic lattices for repulsive biquadratic coupling using Monte Carlo renormalization-group techniques. Two complete phase diagrams are obtained featuring the ferromagnetic, the antiquadrupolar, and–in a narrow region–the novel ferrimagnetic phase. All three phases exhibit re-entrance upon lowering the temperature; in the case of the ferromagnetic phase, double re-entrance is observed.

Europhysics Letters (EPL)•Jan 21, 1992•59 citations

Renormalization-group theory of an internal critical-end-point structure: The Blume-Emery-Griffiths model with biquadratic repulsion

Roland R. Netz, A. Nihat Berker

A prefaced renormalization-group study indicates that all three features of the Blume-Emery-Griffiths model with repulsive biquadratic interaction, namely (1) a critical-end-point structure occurring inside the ferromagnetic phase, (2) disordered-ferromagnetic-disordered reentrance, and (3) a ferrimagnetic phase sandwiched between the ferromagnetic and antiquadrupolar phases, survive fluctuations in three dimensions but not in two dimensions. The renormalization-group mechanism for a critical-end-point structure inside the ordered phase is shown to be the same as that originally found for a critical-end-point structure inside the disordered phase, namely a distinct hybrid fixed point, contrary to a previous claim.

Physical review. B, Condensed matter•Jun 1, 1993•53 citations

Surface critical behavior of the semi-infinite Blume-Emery-Griffiths model

A. Bakchich, M. El Bouziani

Phase transitions of the three-dimensional semi-infinite Blume-Emery-Griffiths model, extended to negative biquadratic interactions, are investigated within the framework of the mean-field approximation in comparison with the real-space renormalization-group results found previously. All the possible qualitative types of phase diagrams characterizing phase transitions of the model, including high entropy ferrimagnetic and staggered quadrupolar phases, have been determined. It is shown that such a system can exhibit critical and tricritical behavior on the surface and multicritical points.

Physical review. B, Condensed matter•Nov 1, 1997•18 citations

Blume-Emery-Griffiths-Potts model in two dimensions: Phase diagram and critical properties from a position-space renormalization group

A. Nihat Berker, Michael Wortis

The spin-1 Ising model on the square lattice with nearest-neighbor ferromagnetic exchange interactions [both bilinear ($J$) and biquadratic ($K$) and crystal-field interaction ($\ensuremath{\Delta}$) is studied via a renormalization-group transformation in position space. The phase diagram in $J$, $K$, $\ensuremath{\Delta}$ space is found to have one surface of critical phase transitions and two surfaces of first-order phase transitions. These surfaces are variously bounded by an ordinary tricritical line, an isolated critical line, and a line of critical end points. These three lines joint at a special tricritical point corresponding to the transition of the three-state Potts model. The over-all phase diagram is qualitatively similar to that obtained with the mean-field approximation, except in the vicinity of the Potts transition where a four-phase coexistence line in mean-field theory shrinks into a special tricritical point in renormalization-group theory. Symmetry considerations guide the construction of our truncated renormalization-group transformation. The global connectivity and local exponents of the thirteen separate fixed points underlying this quite complicated structure are determined. Local analysis with respect to magnetic field ($H$) and another odd interaction ($L$) is performed. A one-adjusted-parameter version of our transformation yields remarkably quantitative results, predicting the Potts transition temperature, for example, within 0.3% of the exact value.

Physical review. B, Solid state•Dec 1, 1976•371 citations

Three-component model and tricritical points: A renormalization-group study. Two dimensions

Miron Kaufman, Robert B. Griffiths, Julia M. Yeomans +1 more

The global phase diagram for a three-component lattice gas or spin-one Ising model with general single-site and nearest-neighbor "ferromagnetic" interactions is worked out for two-dimensional lattices using a Migdal-Kadanoff recursion relation. It differs in important qualitative respects from the corresponding mean-field phase diagram. The set of fixed points and flows provides the characteristic phase diagrams of the three-state Potts multicritical point and the ordinary ($n=1$) tricritical point in a complete set of symmetry-breaking fields. The latter is associated, in this renormalization-group scheme, with seven distinct critical fixed points, a number which is surprisingly large.

Physical review. B, Condensed matter•Apr 1, 1981•104 citations
Phase transitions of a four-component lattice gas or spin-3/2 Blume-Emery-Griffiths model, with a single-ion uniaxial anisotropy and nearest-neighbour pair interactions, both bilinear and biquadratic, are investigated for two-dimensional lattices using an approximate renormalization-group approach of the Migdal-Kadanoff type. The set of fixed points and flows provide the characteristic phase diagrams, in the case of repulsive biquadratic interaction, featuring four ordered phases including high-entropy ferrimagnetic and staggered quadrupolar phases. Successive phase transitions and multicritical points are also found.
Using a renormalization-group transformation in position space based on the Migdal-Kadanoff recursion relations, we investigate the three-dimensional semi-infinite cubic spin-32\frac{3}{2}23​ Blume-Emery-Griffiths model with single-site uniaxial anisotropy and nearest-neighbor pair interactions, both bilinear and biquadratic. The fixed-point topologies and corresponding phase diagrams predicted for this model are presented. Attention is focused on the renormalization-group description of the surface critical behaviors, in comparison with the mean-field approximation results. Three main classes of system phase diagrams are determined, featuring a rich variety of phase transitions associated with the surface with type being according to the values of bulk and surface interaction parameters. Surface critical, tricritical, bicritical, and multicritical points are also found.
A prefaced renormalization-group study indicates that all three features of the Blume-Emery-Griffiths model with repulsive biquadratic interaction, namely (1) a critical-end-point structure occurring inside the ferromagnetic phase, (2) disordered-ferromagnetic-disordered reentrance, and (3) a ferrimagnetic phase sandwiched between the ferromagnetic and antiquadrupolar phases, survive fluctuations in three dimensions but not in two dimensions. The renormalization-group mechanism for a critical-end-point structure inside the ordered phase is shown to be the same as that originally found for a critical-end-point structure inside the disordered phase, namely a distinct hybrid fixed point, contrary to a previous claim.
Phase transitions of the three-dimensional semi-infinite Blume-Emery-Griffiths model, extended to negative biquadratic interactions, are investigated within the framework of the mean-field approximation in comparison with the real-space renormalization-group results found previously. All the possible qualitative types of phase diagrams characterizing phase transitions of the model, including high entropy ferrimagnetic and staggered quadrupolar phases, have been determined. It is shown that such a system can exhibit critical and tricritical behavior on the surface and multicritical points.
The spin-1 Ising model on the square lattice with nearest-neighbor ferromagnetic exchange interactions [both bilinear (JJJ) and biquadratic (KKK) and crystal-field interaction ($\ensuremath{\Delta}$) is studied via a renormalization-group transformation in position space. The phase diagram in JJJ, KKK, $\ensuremath{\Delta}$ space is found to have one surface of critical phase transitions and two surfaces of first-order phase transitions. These surfaces are variously bounded by an ordinary tricritical line, an isolated critical line, and a line of critical end points. These three lines joint at a special tricritical point corresponding to the transition of the three-state Potts model. The over-all phase diagram is qualitatively similar to that obtained with the mean-field approximation, except in the vicinity of the Potts transition where a four-phase coexistence line in mean-field theory shrinks into a special tricritical point in renormalization-group theory. Symmetry considerations guide the construction of our truncated renormalization-group transformation. The global connectivity and local exponents of the thirteen separate fixed points underlying this quite complicated structure are determined. Local analysis with respect to magnetic field (HHH) and another odd interaction (LLL) is performed. A one-adjusted-parameter version of our transformation yields remarkably quantitative results, predicting the Potts transition temperature, for example, within 0.3% of the exact value.
The global phase diagram for a three-component lattice gas or spin-one Ising model with general single-site and nearest-neighbor "ferromagnetic" interactions is worked out for two-dimensional lattices using a Migdal-Kadanoff recursion relation. It differs in important qualitative respects from the corresponding mean-field phase diagram. The set of fixed points and flows provides the characteristic phase diagrams of the three-state Potts multicritical point and the ordinary (n=1n=1n=1) tricritical point in a complete set of symmetry-breaking fields. The latter is associated, in this renormalization-group scheme, with seven distinct critical fixed points, a number which is surprisingly large.