High-temperature expansion of the tetrahedral spin-1/2 and spin-2 XXZ models

Rojas, Onofre; Silva, E. V. Corrêa; Souza, S. M. de; Thomaz, M. T.

doi:10.1103/physrevb.69.134405

Cited by 9 publications

(9 citation statements)

References 28 publications

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“…Now for a complete analyze of the ATIH model, we shall turn our attention to study the XXZ interaction edge for the decorated spin-1. In this situation we have nine eigenvector after diagonalizing the Hamiltonian, corresponding to the eigenvalues (15)(16)(17)(18)(19), thus the normalized eigenvectors are…”

Section: The Xxz Interaction Edge With Spin-1mentioning

confidence: 99%

“…These theoretical results could enhance the other experimental realizations provided by the polymeric compounds such as Cu2OSO4 [13] and M3(OH)2 (with M=Ni, Co, Mn) [14,15]. Other quasi-unidimensional Heisenberg models were studied using numerical results such as discussed in references [12,16] and some analytical series expansion also has been performed [17] for similar systems.…”

Section: Introductionmentioning

confidence: 99%

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Phase diagram of the asymmetric tetrahedral Ising–Heisenberg chain

Valverde

Rojas

Souza

2008

J. Phys.: Condens. Matter

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The asymmetric tetrahedron is composed by all edges of tetrahedron represented by Ising interaction except one, which has a Heisenberg type interaction. This asymmetric tetrahedron is arranged connecting a vertex which edges are only Ising type interaction to another vertex with same structure of another tetrahedron. The process is replicated and this kind of lattice we call the asymmetric Ising-Heisenberg chain. We have studied the ground state phase diagram for this kind of models. Particularly we consider two situations in the Heisenberg-type interaction, (i) The asymmetric tetrahedral spin(1/2,1/2) Ising-XYZ chain, and (ii) the asymmetric tetrahedral spin-(1/2,1) Ising-XXZ chain, where we have found a rich phase diagram and a number of multicritical points. Additionally we have also studied their thermodynamics properties and the correlation function, using the decorated transformation. We have mapped the asymmetric tetrahedral Ising-Heisenberg chain in an effective Ising chain, and we have also concluded that it is possible to evaluate the partition function including a longitudinal external magnetic field.

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Section: The Xxz Interaction Edge With Spin-1mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Phase diagram of the asymmetric tetrahedral Ising–Heisenberg chain

Valverde

Rojas

Souza

2008

J. Phys.: Condens. Matter

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“…The presence of spin S = 0 in a given site of the chain can be interpreted as nonmagnetic impurity at that site [6].…”

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confidence: 99%

“…[6], the presence of a spin S = 0 in a site of the chain can be interpreted as nonmagnetic impurity at that site. The model thus encompasses the presence of randomly distributed impurities along the chain, without hindering the application of the method of Ref.…”

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Thermodynamics of the spin ladder as a composite chain model

Rojas

Silva

Souza

et al. 2005

Physica A: Statistical Mechanics and its Applications

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A special class of S = 1 spin ladder hamiltonians, with second-neighbor exchange interactions and with anisotropies in the z-direction, can be mapped onto one-dimensional composite S = 2 (tetrahedral S = 1) models. We calculate the high temperature expansion of the Helmoltz free energy for the latter class of models, and show that their magnetization behaves closely to that of standard XXZ models with a suitable effective spin S ef f , such that S ef f (1 + S ef f ) = S 2 i , where S i refers to the components of spin in the composite model. It is also shown that the specific heat per site of the composite model, on the other hand, can be very different from that of the effective spin model, depending on the parameters of the hamiltonian. Many materials have been described by low-dimensional spin models[1] such as XXZ, ladder, tetrahedral, dimmer chain, and mixed spin models. Different predictions are obtained from one-dimensional and quasi-one-dimensional models that can be verified experimentally; e.g., the S = 1/2 antiferromagnetic Heisenberg chain is a gapless model, whereas the even-legged antiferromagnetic Heisenberg ladder model has a gap in its energy spectrum [2]. Attention has also been drawn to composite spin models; for instance, the T = 0 phase diagram for the * Corresponding author: mtt@if.uff.br 2 S = (1/2⊕1/2) model has been studied by Sólyom and Timonen[3,4]. This composite spin model is equivalent to the tetrahedral S = 1/2 model -applied to the study of the properties of the tellurate materials Cu 2 T e 2 O 5 Cl 5 and Cu 2 T e 2 O 5 Br 5 . On the basis of experimental results it was argued that these materials could be appropriately described by the noninteracting tetrahedral S = 1/2 model [5]. In Ref.[6] we obtained the high temperature expansion of the Helmholtz free energy of the tetrahedral S = 1/2 model up to order β 5 .A common feature shared by all composite spin models is that the modulus of the spin at each site of the chain is not constant; instead, one has a random distribution throughout the chain. The presence of spin S = 0 in a given site of the chain can be interpreted as nonmagnetic impurity at that site [6].By the appropriate design of molecules, it is possible to obtain a variety of spin systems. One example is the organic compound BIP-TENO [7], found to be a S = 1 spin ladder. At T = 0 this compound exhibits a plateau-like anomaly at 1/4 of the saturation magnetization, which has attracted much attention due to its full quantum nature. In Ref. The hamiltonian of the quasi-one-dimensional spin model isand it is subject to periodic boundary conditions. We use the same notation as in Ref.[6]:, introducing the anisotropy in the z-direction. For ∆ 0 = 1 and ∆ = 1, (1) equals to the sum of hamiltonians (2) and (3) of reference [8] for the S = 1 ladder with second-neighbor exchanges (J 3 = 0), for the special case J 1 = J 2 . The distinct S = 1 variables σ i and τ i are related to the ρ-and r-lines of the dumb-bell, respectively (cf. Fig.1 of Ref.[6]).We define the composite spin ...

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