Exactly solved mixed spin-(1,1/2) Ising–Heisenberg diamond chain with a single-ion anisotropy

Lisnyi, Bohdan; Strečka, Jozef

doi:10.1016/j.jmmm.2014.10.113

Cited by 15 publications

(13 citation statements)

References 42 publications

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“…To date, exact solutions have been found for various complex models based on the 1D Ising model. They includes Blume-Emery-Griffiths model [1][2][3] , the model with localized Ising-like spins and exchanging electrons 4 , the models with single-ion anisotropy for the spin-1 chain [5][6][7] or the mixed spin-1/2 and spin-1 Ising chain [8][9][10] , the Ising-Heisenberg "decorated" chains, ladders, and tubes [11][12][13][14][15][16][17][18][19][20] and the Ising-Hubbard diamond chain and ladder 21,22 . These systems show many subtle and important phenomena, including quantized plateaux in the magnetization curves, quantum entanglement, quasi-phases and pseudo-transitions 23 , and describe the properties of real materials, such as the polymeric coordination compounds (see Refs.…”

Section: Introductionmentioning

confidence: 99%

Local distributions of the 1D dilute Ising model

Panov

2020

Journal of Magnetism and Magnetic Materials

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The local distributions of the one-dimensional dilute annealed Ising model with charged impurities are studied. Explicit expressions are obtained for the pair distribution functions and correlation lengths, and their low-temperature asymptotic behavior is explored depending on the concentration of impurities. For a more detailed consideration of the ordering processes, we study local distributions. Based on the Markov property of the dilute Ising chain, we obtain an explicit expression for the probability of any finite sequence and find a geometric probability distribution for the lengths of sequences consisting of repeating blocks. An analysis of distributions shows that the critical behavior of the spin correlation length is defined by ferromagnetic or antiferromagnetic sequences, while the critical behavior of the impurity correlation length is defined by the sequences of impurities or by the charge-ordered sequences. For the dilute Ising chain, there are no other repeating sequences whose mean length diverges at zero temperature. While both the spin correlation and the impurity correlation lengths can diverge only at zero temperature, the ordering processes result in a maximum of the specific heat at finite temperature defined by the maximum rate of change of the impurity-spin pairs concentration. A simple approximate equation is found for this temperature. We show that the non-ordered dilute Ising chains correspond to the regular Markov chains, while various orderings generate the irregular Markov chains of different types.

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Section: Introductionmentioning

confidence: 99%

Local distributions of the 1D dilute Ising model

Panov

2020

Journal of Magnetism and Magnetic Materials

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“…The magnetization curves, thus, for the Ising-Heisenberg spin systems share almost all features with the magnetization curves of the small spin clusters, but can contain much more intermediate magnetization plateaus. Various variants of the Ising-Heisenberg chains have been examined: diamond-chain, [14][15][16][17][18][19][20][21][22][23][24][25][26][27][28] saw-tooth chain, 29,30 orthogonal-dimer chain, [31][32][33] tetrahedral chain, [34][35][36][37][38] and some special examples relevant to real magnetic materials. [39][40][41][42] In the present work, we will rigorously examine a magnetization process of a few quantum Heisenberg spin clusters and Ising-Heisenberg diamond chain, which will not display strict magnetization plateaus on assumption that some constituent spins have different Landé g-factors and may be a XY-anisotropy of the exchange interaction.…”

Section: Introductionmentioning

confidence: 99%

Absence of actual plateaus in zero-temperature magnetization curves of quantum spin clusters and chains

et al. 2015

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We examine the general features of the non-commutativity of the magnetization operator and Hamiltonian for the small quantum spin clusters. The source of this non-commutativity can be a difference in the Landé g-factors for different spins in the cluster, XY-anisotropy in the exchange interaction and the presence of the Dzyaloshinskii-Moriya term in the direction different from the direction of the magnetic field. As a result, zero-temperature magnetization curves for small spin clusters mimic those for the macroscopic systems with the band(s) of magnetic excitations, i.e. for the given eigenstate of the spin cluster the corresponding magnetic moment can be an explicit function of the external magnetic field yielding the non-constant (non-plateau) form of the magnetization curve within the given eigenstate. In addition, the XY-anisotropy makes the saturated magnetization (the eigenstate when all spins in cluster are aligned along the magnetic field) inaccessible for finite magnetic field magnitude (asymptotical saturation). We demonstrate all these features on three examples: spin-1/2 dimer, mixed spin-(1/2,1) dimer, spin-1/2 ring trimer. We consider also the simplest Ising-Heisenberg chain, the Ising-XYZ diamond chain with four different g-factors. In the chain model the magnetization curve has a more complicated and non trivial structure which that for clusters.

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“…{J 1 , J 2 , J 3 } rigorous proof that the striking magnetization plateaus proposed in Ref. [40] cannot appear neither in the generalized mixed spin-(1,1/2) Ising-Heisenberg diamond chain, which accounts for the single-ion anisotropy acting on the nodal spin-1 atoms [42].…”

Section: Introductionmentioning

confidence: 74%

“…The Boltzmann's factor (8) can be subsequently replaced through the generalized decoration-iteration transformation [43][44][45][46] similarly as we have done this before [41,42]. But since this Boltzmann's factor is essentially a transfer matrix (see eq.…”

Section: Model and Its Exact Solutionmentioning

confidence: 99%