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Europhysics Letters (EPL)

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

Roland R. Netz

Published Jan 21, 1992• 59 citations
Publisher

Abstract

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.

DOI
10.1209/0295-5075/17/4/016

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Physical review. B, Condensed matter•Nov 1, 1997•18 citations
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.
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 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.
The critical behaviour of the ferromagnetic spin-3/2 Blume-Emery-Griffiths model with repulsive biquadratic coupling in the absence and presence of an external magnetic field is studied by using the lowest approximation of the cluster variation method, which is identical with the mean-field approximation. Thermal variations of the order parameters are investigated for different values of the interaction parameters and the external magnetic field. The complete phase diagrams of the system are calculated in the (kT/J,K/J), (kT/J,D/J) and (kT /J,H/J) planes. Five new phase diagram topologies are obtained, which are either absent from previous approaches or have gone unnoticed. A detailed discussion and comparison of the phase diagrams is made.
Abstract We use the Monte Carlo simulation technique to study the critical behavior of a three-state spin model, with bilinear and biquadratic nearest-neighbor interactions, known as the Blume–Emery–Griffiths model (BEG), in a square lattice. In order to characterize this model, we study the phase diagram, in which we identify three different phases: ferromagnetic, paramagnetic and quadrupolar, the later with one sublattice filled with spins and the other with vacancies. We perform our studies by using two algorithms: Metropolis update (MU) and Wang–Landau (WL). The critical scaling behavior of the model is complementary studied by applying results obtained by using both algorithms, while tricritical points and the tricritical scaling behavior is analyzed by means of WL measuring the joint density of states and using the method of field mixing in conjunction with finite-size scaling. Furthermore, motivated by the decoupling between spins observed within the quadrupolar phase, we further generalize the BEG model in order to study the behavior of the system by adding a next nearest neighbour (NNN) interaction between spins. We found that by increasing the strength of the (ferromagnetic) NNN interaction, a new ferromagnetic phase takes over that contains both quadrupolar and ferromagnetic order.
We investigated the dynamic phase transitions (DPTs) in the mixed spin (2, 5/2) Blume-Emery Griffiths model with repulsive biquadratic interaction in the presence of a time-varying magnetic field. We used the path probability method to obtain the set of the dynamic equations. We numerically solved these dynamic equations to characterize the nature of first- and second-order phase transitions and to find the DPT temperatures as well as obtain the phases in the system. We constructed the dynamic phase diagrams (DPDs) in reduced temperature and amplitude of oscillating magnetic field plane. We observed that the DPDs display richer, complex and more topological various type of phase diagrams. In particular, DPDs exhibit the disordered phase, antiquadrupolar or staggered phase, six different ferrimagnetic phases, three different nonmagnetic phases, and numerous mixed phases. DPDs also display two dynamic tricritical points for only smaller values of crystal-field interactions, multiple critical end and double critical end points, one zero-temperature critical point, one inverse critical end point, and a quadruple point depending on interaction parameters. The system always shows the reentrant behaviors for the higher values of magnetic field amplitude, but it does not exhibit the dynamic tricritical behavior for higher values of crystal-field parameter.
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.