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Monte Carlo Study of a Spin-3/2 Blume-Emery-Griffiths Model on a Honeycomb Lattice

Published Feb 16, 2016• 3 citations
OpenAlex

Abstract

We study the phase diagram of the spin-3/2 Blume-Emery-Griffiths model on a honeycomb lattice by Monte Carlo simulations in order to verify the presence of some peculiar features predicted by the effective field theory (EFT) with correlations. The locations of the order-disorder phase boundaries are estimated from thermal varia-tions of the magnetic susceptibility curves. It is found that for positive values of the biquadratic interactions the critical boundary shows a discontinuous character as a function of the single-ion anisotropy strength, in line with the EFT expectations. However, for negative values of the biquadratic interactions the step-like variation of the critical frontier predicted by EFT was not reproduced.

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We study the phase diagram of the spin-3/2 Blume-Emery-Griffiths model on a honeycomb lattice by Monte Carlo simulations in order to verify the presence of some peculiar features predicted by the effective field theory (EFT) with correlations. The locations of the order-disorder phase boundaries are estimated from thermal varia-tions of the magnetic susceptibility curves. It is found that for positive values of the biquadratic interactions the critical boundary shows a discontinuous character as a function of the single-ion anisotropy strength, in line with the EFT expectations. However, for negative values of the biquadratic interactions the step-like variation of the critical frontier predicted by EFT was not reproduced.
We study the phase diagram of the spin-3/2 Blume-Emery-Griths model on a honeycomb lattice by Monte Carlo simulations in order to verify the presence of some peculiar features predicted by the eective eld theory (EFT) with correlations.The locations of the order-disorder phase boundaries are estimated from thermal variations of the magnetic susceptibility curves.It is found that for positive values of the biquadratic interactions the critical boundary shows a discontinuous character as a function of the single-ion anisotropy strength, in line with the EFT expectations.However, for negative values of the biquadratic interactions the step-like variation of the critical frontier predicted by EFT was not reproduced.
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.
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 effect of the random quantum transverse field Ω on the tricritical behavior of the spin-1 Blume–Emery–Griffiths (BEG) model is studied using an effective field theory. It is found that the tricritical behavior depends on both the biquadratic interaction K, single-ion anisotropy Δ and the concentration p of the disorder of Ω. Indeed, there exists a special value p1 of the probability p below which the tricritical behavior disappears. In addition, at sufficiently low temperatures, the system exhibits long-range order accompanied by the tricritical behavior below a special value p2 of the probability p.