Exact solutions for Ising-model correlations in the 3-12 (extended<i>kagome</i>´) lattice

Barry, J. H.; Khatun, Mahfuza

doi:10.1103/physrevb.51.5840

Cited by 42 publications

(40 citation statements)

References 15 publications

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“…It can be straightforwardly proved by adopting the exact mapping theorems developed by Barry et al [37][38][39][40] that the sublattice magnetization of the Ising spins within the spin-1/2 Ising-Heisenberg model on triangulated Husimi lattices directly equals to the spontaneous magnetization of the effective spin-1/2 Ising model on pure Husimi lattices…”

Section: Model and Methodsmentioning

confidence: 99%

Presence or absence of order by disorder in a highly frustrated region of the spin-1/2 Ising-Heisenberg model on triangulated Husimi lattices

Strečka

Ekiz

2015

Phys. Rev. E

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The geometrically frustrated spin-1/2 Ising-Heisenberg model on triangulated Husimi lattices is exactly solved by combining the generalized star-triangle transformation with the method of exact recursion relations. The ground-state and finite-temperature phase diagrams are rigorously calculated along with both sublattice magnetizations of the Ising and Heisenberg spins. It is evidenced that the Ising-Heisenberg model on triangulated Husimi lattices with two or three inter-connected triangles-in-triangles units displays in a highly frustrated region a quantum disorder irrespective of temperature, whereas the same model on triangulated Husimi lattices with a greater connectivity of triangles-in-triangles units exhibits at low enough temperatures an outstanding quantum order due to the order-by-disorder mechanism. The quantum reduction of both sublattice magnetizations in the peculiar quantum ordered state gradually diminishes with increasing the coordination number of underlying Husimi lattice.

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Section: Model and Methodsmentioning

confidence: 99%

Presence or absence of order by disorder in a highly frustrated region of the spin-1/2 Ising-Heisenberg model on triangulated Husimi lattices

Strečka

Ekiz

2015

Phys. Rev. E

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“…Moreover, in a molecular layer of JT quasiparticles constructed in such a way that it preserves the symmetry for a coherent JT effect (for instance, in the case of C3 local symmetry point group, each of the JT centers must have three nearest-neighbors, and form a kind of the kagomé or the 3-12 lattices [20,21]) the unique dynamics of the 1/2-fractional statistics can be preserved. The wave of molecular distortions of the lattice of the JT centers is of a special kind.…”

Section: Discussionmentioning

confidence: 99%

Jahn-Teller Center as Quasiparticle of Fractional Statistics

Sobolewski

1995

Acta Phys. Pol. A

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“…The square, Kagomé, honeycomb, triangular and 3-12 Ising lattices are the most studied structures to our knowledge, see e.g. [4,[8][9][10][11][12]. The timeindependent, short-range spin correlations on the two-dimensional Ising ferromagnetic systems are exactly calculated by many researchers.…”

Section: Introductionmentioning

confidence: 99%

Vacancy Migration in the 3-12 Ising Ferromagnet

Khatun

Emert

2002

phys. stat. sol. (b)

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A theoretical study of the temperature-dependent magnetic contributions to the free enthalpy, entropy, and enthalpy of vacancy migration for 3-12 ferromagnetic Ising system is presented. The exact solutions of spin correlations for the perfect 3-12 structure enable determination of the thermodynamic functions at all temperatures. The nonequivalent edge effect on vacancy migration of the structure is also reported. The magnetic contributions to the thermodynamic functions of vacancy migration are more pronounced in the compact part of the structure. In general, the entropy and enthalpy diverge at the critical temperature; the free enthalpy decreases monotonically with temperature with a singular behavior at the critical temperature.

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Exact solutions for Ising-model correlations in the 3-12 (extendedkagome´) lattice

Cited by 42 publications

References 15 publications

Presence or absence of order by disorder in a highly frustrated region of the spin-1/2 Ising-Heisenberg model on triangulated Husimi lattices

Presence or absence of order by disorder in a highly frustrated region of the spin-1/2 Ising-Heisenberg model on triangulated Husimi lattices

Jahn-Teller Center as Quasiparticle of Fractional Statistics

Vacancy Migration in the 3-12 Ising Ferromagnet

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