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arXiv:cond-mat/0507177 · physica status solidi (b)

Magnetization and quadrupolar plateaus in the one‐dimensional antiferromagnetic spin‐3/2 and spin‐2 Blume–Capel model

Ekrem Aydıner, Cenk Akyüz, Meltem Gönülol, Hamza Polat

Published Sep 21, 2006• 13 citations
arXivHTMLPDF

Abstract

Abstract We employed the classical transfer matrix technique to investigate the magnetization and quadrupolar plateaus, phase diagrams and other thermodynamical properties of the one‐dimensional antiferromagnetic spin‐3/2 and spin‐2 Blume–Capel model in the presence of an external magnetic field at very low temperatures. We showed that single‐ion anisotropy is one of the indispensable ingredients for an energy gap which causes to magnetization and quadrupolar plateaus in one‐dimensional antiferromagnetic Ising spin chains. Other thermodynamical predictions seem to be provide this argument. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

DOI
10.1002/pssb.200541252

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Abstract We employed the classical transfer matrix technique to investigate the magnetization and quadrupolar plateaus, phase diagrams and other thermodynamical properties of the one‐dimensional antiferromagnetic spin‐3/2 and spin‐2 Blume–Capel model in the presence of an external magnetic field at very low temperatures. We showed that single‐ion anisotropy is one of the indispensable ingredients for an energy gap which causes to magnetization and quadrupolar plateaus in one‐dimensional antiferromagnetic Ising spin chains. Other thermodynamical predictions seem to be provide this argument. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Abstract In this paper a self‐consistent mean‐field approximation is used to study the thermodynamic properties of a spin‐1 antiferromagnetic Heisenberg chain with an anisotropy in the presence of an external magnetic field at a finite temperature. The temperature dependences of the internal energy, Haldane gap, and correlation length are presented. It is found that the internal energy and Haldane gap increase with increasing temperature, while the correlation length decreases for a fixed magnetic field and single‐ion anisotropy. The magnetic field splits the Haldane gap into two branches: the upper branch increases with increasing magnetic field while the other branch decreases. The numerical results are consistent with those of other theoretical methods. (© 2003 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
We study the one-dimensional S = 1 Blume-Emery-Griffiths model.Upon transforming the spin model into an equivalent fermionic model, we provide the exact solution within the Green's function and equations of motion formalism.We show that the relevant response functions as well as thermodynamic quantities can be determined, in the whole parameters space, in terms of a finite set of local correlators.Furthermore, considering the case of an antiferromagnetic chain with single-ion anisotropy in the presence of an external magnetic field, we find three plateaus in the magnetization curve.In the neighborhood of the endpoints of the intermediate plateau, the specific heat shows a double peak structure.
We have studied the presence of plateaus on the low-temperature magnetization of an antiferromagnetic spin-1 chain, as an external uniform magnetic field is varied. A crystal-field interaction is present in the model and the exchange constants follow a random quenched (Bernoulli or Gaussian) distribution. Using a transfer-matrix technique we calculate the largest Lyapunov exponent and, from it, the magnetization at low temperatures as a function of the magnetic field, for different values of the crystal field and the width of the distributions. For the Bernoulli distribution, the number of plateaus increases, with respect to the uniform case [Litaiff et al., Solid State Commun. 147, 494 (2008)] and their presence can be linked to different ground states, when the magnetic field is varied. For the Gaussian distributions, the uniform scenario is maintained, for small widths, but the plateaus structure disappears as the width increases.
Abstract We investigate the density of states (DOS) in an antiferromagnetic spin‐system on a square lattice described by the Blume–Capel (BC) model. We use a new and very efficient simulation method, proposed by Wang and Landau, in which we estimate very precisely DOS by sampling in the space of energy. Then we calculate the thermodynamical averages like internal energy, free energy, specific heat and entropy. The BC model exhibits multicritical behaviour such as first‐ or second‐order transitions and tricritical points. It is known that the ground state of the model can exhibit two kinds of staggered antiferromagnetic phases: AF 1 (two interpenetrating lattices with S = –1 and S = 1) and AF 2 ( S = –1 and S = 0 for H < 0; S = 1 and S = 0 for H > 0). We analyze the coexistence of such phases at finite temperatures and determine border lines between them. To understand the microscopic nature of such boundaries we present also some results obtained with the standard Monte Carlo method. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
To investigate the magnetization and the effect of anisotropy on thermal properties in external magnetic field,the transfer matrix method is used to calculate exactly the solution to the magnetization in Ising spin ladder with S=1 and S=3/2 mixed together.It's found that if the closest neighboring interaction is ferromagnetic and the next closest interaction between two spin chains is antiferromagnetic,the plateaus of the magnetization m=1/4 and m=3/4 appear in the system,which are consistent with the positions where the magnetization plateaus are possibly appearing in quantum model.Novel dual-peak is observed on the curves of specific heat and susceptibility.
The zero-temperature phase diagram of a one-dimensional S=2S=2S=2 Heisenberg ferromagnet with single-ion cubic anisotropy is studied numerically using the density-matrix renormalization-group method. Evidence is found that although the model does not involve quadrupolar couplings, there is a purely quadrupolar phase for large values of the anisotropy. The phase transition between the magnetic and quadrupolar phases is continuous and it seems to be characterized by Ising critical exponents.