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arXiv:0812.0127 · Physics of Atomic Nuclei

Phase diagrams of the Ising-Heisenberg chain with S = 1/2 triangular XXZ clusters

Vadim Ohanyan

Published Mar 1, 2010• 15 citations
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Abstract

The one-dimensional spin system consisted of triangular S = 1/2 XXZ Heisenberg clusters alternating with single Ising spins is considered. Partition function of the system is calculated exactly within the transfer-matrix formalism. T = 0 ground state phase diagrams, corresponding to different regions of the values of system parameters, are obtained.

DOI
10.1134/s1063778810030129

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The one-dimensional spin system consisted of triangular S = 1/2 XXZ Heisenberg clusters alternating with single Ising spins is considered. Partition function of the system is calculated exactly within the transfer-matrix formalism. T = 0 ground state phase diagrams, corresponding to different regions of the values of system parameters, are obtained.
A mixed Ising-Heisenberg spin system consisting of triangular XXZXXZXXZ-Heisenberg spin clusters assembled into a chain by alternating with Ising spins interacting to all three spins in the triangle is considered. The exact solution of the model is given in terms of the generalized decoration-iteration map and within the transfer-matrix technique. Exact expressions for thermodynamic functions are derived. Ground-state phase diagrams and thermodynamic and magnetic properties of the system are examined.
The asymmetric tetrahedron is composed of all edges of a tetrahedron represented by Ising interactions except for one, which has a Heisenberg-type interaction. This asymmetric tetrahedron is arranged by connecting a vertex whose edges are only Ising-type interactions to another vertex with the same structure for 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 model. In particular, 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 thermodynamical 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.
We study a spin-1/2 model with triangular XXZXXZXXZ clusters on the orthogonal-dimer chain in the presence of an external magnetic field. First, we discuss the case where the triangular clusters are coupled via intermediate ``classical'' Ising spins. Diagonalization of the triangular XXZXXZXXZ clusters yields the exact ground states; finite-temperature properties are computed exactly by an additional transfer-matrix step. A detailed analysis reveals a large variety of ground states at magnetization MMM equal to fractions 0, 1/41/41/4, and 1/21/21/2 of the saturation magnetization M=1M=1M=1. Some of these ground states break translational symmetry spontaneously and give rise to doubling of the unit cell. In a second part, we present complementary numerical data for the spin-1/2 Heisenberg model on the orthogonal-dimer chain. We analyze several examples of T=0T=0T=0 magnetization curves, entropy as a function of temperature TTT and magnetic field, and the associated magnetic cooling rate. Comparison of the two models shows that in certain situations the simplified exactly solvable model yields a qualitatively or sometimes even quantitatively accurate description of the more challenging quantum model, including a case which may be relevant to experimental observations of an enhanced magnetocaloric effect in the two-dimensional compound SrCu2{}_{2}2​(BO3{}_{3}3​)2{}_{2}2​.
The one-dimensional S=1 quantum spin system has been mapped onto the equivalent two-dimensional Ising model on the basis of the equivalence theorem of Suzuki. The classical representation of the partition function has been expressed in terms of the maximum eigenvalue of the transfer matrix and evaluated by means of the numerically exact transfer-matrix method. The physical meaning of two kinds of correlation functions in RSD and CBD has been made clear in terms of the concept of the maximum eigenstate. Calculations have been made for both ferromagnetic and antiferromagnetic Heisenberg chains with several single-site anisotropy values, both positive and negative. Good agreements are found with some existing numerical results.