Reentrant Transitions of Ising-Heisenberg Ferromagnet on a Triangular Lattice with Diamond-Like Decorations

Jaščur, M.; Strečka, Jozef; Čanová, Lucia

doi:10.12693/aphyspola.113.453

Cited by 8 publications

(19 citation statements)

References 5 publications

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“…It is worth mentioning that all obtained results are universal as they hold regardless of whether ferromagnetic or antiferromagnetic interaction parameters J I and J H are assumed, as well as, independently of the lattice topology or spatial dimensionality of the investigated spin system. As proved, however, there are some fundamental differences between magnetic behaviour of models with distinct nature of the Heisenberg interaction (see our preliminary reports 32, 35, 36). Considering this fact, we will restrict ourselves here just to the case with the ferromagnetic Heisenberg interaction J H > 0.…”

Section: Resultsmentioning

confidence: 74%

“…Unfortunately, searching for the exact solution for the geometrically frustrated quantum Heisenberg models often fails due to a non‐commutability between spin operators involved in their Hamiltonians. Owing to this fact, we have recently proposed a special class of geometrically frustrated Ising–Heisenberg models on diamond‐like decorated lattices 32–38, which can be examined within the framework of an exact analytical approach based on the generalised decoration–iteration transformation 39–41. These simplified quantum models overcome the afore‐mentioned mathematical difficulty by introducing the Ising spins at nodal lattice sites and the Heisenberg dimers on interstitial decorating sites of the considered planar lattice.…”

Section: Introductionmentioning

confidence: 99%

“…It is worth mentioning that the mixed‐spin Ising–Heisenberg models with diamond‐like decorations turn out to be very useful testing ground for elucidating many quantum properties of low‐dimensional magnetic materials, in spite of the fact that the monomer–dimer interaction is considered as the Ising‐type interaction. Indeed, these rather simple spin models shed light on diverse quantum features to appear in the ground state 32–35, 38, the magnetisation process 34, 37, 38, the thermodynamics 34, 37, as well as, the critical behaviour 36. Note that kinetically frustrated diamond chain models constituted by nodal Ising spins and mobile electrons delocalised over the interstitial decorating sites have been particularly examined as well 42–44.…”

Section: Introductionmentioning

confidence: 99%

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Reentrant phenomenon in the exactly solvable mixed spin-1/2 and spin-1 Ising-Heisenberg model on diamond-like decorated planar lattices

Čanová

Strečka

2010

Phys. Status Solidi (b)

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Ground-state and finite-temperature behaviour of the mixed spin-1/2 and spin-1 Ising-Heisenberg model on decorated planar lattices consisting of inter-connected diamonds is investigated by means of the generalised decoration-iteration mapping transformation. The obtained exact results clearly point out that this model has a rather complex ground state composed of two unusual quantum phases, which is valid regardless of the lattice topology as well as the spatial dimensionality of the investigated system. It is shown that the diamond-like decorated planar lattices with a sufficiently high coordination number may exhibit a striking critical behaviour including reentrant phase transitions with two or three consecutive critical points.Copyright line will be provided by the publisher 1 Introduction Quantum Heisenberg models on geometrically frustrated planar lattices have enjoyed a great interest during the past decades especially due to their extraordinary diverse ground-state behaviour, which is often a result of mutual interplay between geometric frustration and quantum fluctuations [1,2,3]. From this perspective, geometrically frustrated quantum systems represent an excellent play ground for theoretical study of novel quantum many-body phenomena. Beside a rather complex ground state, which can be composed of several phases like the semi-classical Néel-like ordered phase, the quantum valence bond crystal phase or different disordered spin-liquid phases [1], quantum spin systems on two-dimensional geometrically frustrated lattices furnish a deeper insight into the quantum order-from-disorder effect [1,2,3], the scalar or vector chirality [4,5], as well as, the non-zero residual entropy that characterizes the macroscopic degeneracy of the ground state [1].

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Section: Resultsmentioning

confidence: 74%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Reentrant phenomenon in the exactly solvable mixed spin-1/2 and spin-1 Ising-Heisenberg model on diamond-like decorated planar lattices

Čanová

Strečka

2010

Phys. Status Solidi (b)

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“…(12)-(13), the former ket vector unambiguously determines the states of four nodal Ising spins from an elementary square face of the pth octahedron and the latter ket vector unambiguously specifies the relevant state of the Heisenberg spin pair. It should be also noticed that another equivalent representations of these eigenstates can be obtained from the eigenvectors (12)- (13) under the reversal of all four nodal Ising spins and consequently, the phases |I and |II are both four-fold degenerate.…”

Section: Resultsmentioning

confidence: 99%

Weak-universal critical behavior and quantum critical point of the exactly soluble spin-1∕2 Ising-Heisenberg model with the pair XYZ Heisenberg and quartic Ising interactions

Strečka¹,

Čanová²,

Minami³

2009

AIP Conference Proceedings

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Spin-1/2 Ising-Heisenberg model with XY Z Heisenberg pair interaction and two different Ising quartic interactions is exactly solved with the help of the generalized star-square transformation, which establishes a precise mapping equivalence with the corresponding eight-vertex model on a square lattice generally satisfying Baxter's zero-field (symmetric) condition. The investigated model exhibits a remarkable weak-universal critical behavior with two marked wings of critical lines along which critical exponents vary continuously with the interaction parameters. Both wings of critical lines merge together at a very special quantum critical point of the infinite order, which can be characterized through diverging critical exponents. The possibility of observing reentrant phase transitions in a close vicinity of the quantum critical point is related to a relative strength of the exchange anisotropy in the XY Z Heisenberg pair interaction. FIGURE 1. The elementary unit cell of the spin-1/2 Ising-Heisenberg model. Full (empty) circles denote positions of the Heisenberg (Ising) spins, thick solid line represents the pairwise XY Z Heisenberg interaction between the apical Heisenberg spins and both types of broken lines connect spins involved in the quartic Ising interactions. Thin solid lines connecting four Ising spins are guide for eyes only.This paper is so organized. In the following section, we will describe the hybrid Ising-Heisenberg model and recall basic steps of the exact mapping procedure to the zero-field eight-vertex model. The most interesting results for the ground-state and finite-temperature phase diagrams, which are supported by a detailed analysis of critical exponents, are subsequently presented in the next section. Finally, some concluding remarks are mentioned along with a brief summary of the most important scientific achievements in the last section. 0 1 2 3 4 0.00 0.05 0.10 0.15 J 2 / J z = 1.0 0.5 0.5 0.25 0.25 J y / J x = 0.5 J 1 / J z = 1.0 J x / J z I II k B T c / J z FIGURE 3. The dimensionless critical temperature as a function of the anisotropy parameter J x /J z for the Ising-Heisenberg model with the XY Z exchange anisotropy (J x = J y ) when a strength of the one quartic Ising-type interaction is fixed (J 1 /J z = 1.0) and that of another one quartic Ising-type interaction J 2 /J z varies.

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“…It is also worth mentioning that the Ising-Heisenberg models on the diamond-like decorated lattices have turned out to be a very useful testing ground for elucidating several typical quantum features. Indeed, these interesting but still exactly tractable spin systems may exhibit diverse quantum ordered and disordered ground states [11-15, 18, 19], the multi-step magnetization process with quantized intermediate magnetization plateaus [14,17,18], the enhanced magnetocaloric effect [14,18], as well as the non-trivial criticality [13,16,19].…”

Section: Introductionmentioning

confidence: 99%

Phase transitions of geometrically frustrated mixed spin-1/2 and spin-1 Ising-Heisenberg model on diamond-like decorated planar lattices

Gálisová¹,

Strečka²

2011

Condens. Matter Phys.

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Phase transitions of the mixed spin-1/2 and spin-1 Ising-Heisenberg model on several decorated planar lattices consisting of interconnected diamonds are investigated within the framework of the generalized decoration-iteration transformation. The main attention is paid to the systematic study of the finite-temperature phase diagrams in dependence on the lattice topology. The critical behaviour of the hybrid quantum-classical Ising-Heisenberg model is compared with the relevant behaviour of its semi-classical Ising analogue. It is shown that both models on diamond-like decorated planar lattices exhibit a striking critical behaviour including reentrant phase transitions. The higher the lattice coordination number is, the more pronounced reentrance may be detected.

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Reentrant Transitions of Ising-Heisenberg Ferromagnet on a Triangular Lattice with Diamond-Like Decorations

Cited by 8 publications

References 5 publications

Reentrant phenomenon in the exactly solvable mixed spin-1/2 and spin-1 Ising-Heisenberg model on diamond-like decorated planar lattices

Reentrant phenomenon in the exactly solvable mixed spin-1/2 and spin-1 Ising-Heisenberg model on diamond-like decorated planar lattices

Weak-universal critical behavior and quantum critical point of the exactly soluble spin-1∕2 Ising-Heisenberg model with the pair XYZ Heisenberg and quartic Ising interactions

Phase transitions of geometrically frustrated mixed spin-1/2 and spin-1 Ising-Heisenberg model on diamond-like decorated planar lattices

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