Exact solutions for Ising-model odd-number correlations on planar lattices

Barry, J. H.; Tanaka, Tomoyasu; Khatun, Mahfuza; Múnera, C. H.

doi:10.1103/physrevb.44.2595

Cited by 52 publications

(40 citation statements)

References 24 publications

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“…However, the exact spin identities and mapping theorems considerably simplify calculation of a large number of quantities. It can be easily proved using the exact mapping theorems developed by Barry et al [32][33][34][35] that the sublattice magnetization, the quadrupolar moment or any other higher order correlation function for the Ising spins in the mixed-spin IsingHeisenberg model on the diamond-like decorated Bethe lattice directly equals to the corresponding quantity on the equivalent spin-1 BEG model on the simple Bethe lattice (of course, this exact mapping holds just if the corresponding model is considered with the effective temperature-dependent interactions J, K and D given by Eqs. (5) and (6)).…”

Section: Model and Its Exact Solutionmentioning

confidence: 98%

Phase diagrams of the mixed spin-1 and spin-1/2 Ising–Heisenberg model on the diamond-like decorated Bethe lattice

Ekiz

Strečka

Jaščur

2011

Journal of Magnetism and Magnetic Materials

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Section: Model and Its Exact Solutionmentioning

confidence: 98%

Phase diagrams of the mixed spin-1 and spin-1/2 Ising–Heisenberg model on the diamond-like decorated Bethe lattice

Ekiz

Strečka

Jaščur

2011

Journal of Magnetism and Magnetic Materials

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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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“…To develop such identities systematically, one proceeds to derive their basic generating equation. [18][19][20][21][22][23][24] Let [f ] be any function of the chain Ising variables µ 1 , µ 2 , . .…”

Section: Spatially Anisotropic Quantum Spin Ladder Model 2003mentioning

confidence: 99%

Exact Solutions in a Spatially Anisotropic Quantum Spin Ladder Model Having Two- And Four-Spin Exchange Interactions

Barry

Cohen

Meisel

2009

Int. J. Mod. Phys. B

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We consider a two-leg S = 1/2 quantum spin ladder model with two-spin (intra-rung) and four-spin (inter-rung) Heisenberg exchange interactions and a uniform magnetic field. Exact mappings are derived connecting the partition function and correlations in the three-parameter quantum model to those known in a two-parameter Ising chain. The quantum phase diagram of the ladder magnet is determined. Static correlations provide pertinent correlation lengths and underlie spatial fluctuation behaviors at arbitrary temperatures, including quantum fluctuations at absolute zero. Dynamic correlations in zero field are used to obtain an exact solution for the inelastic neutron scattering function S xx (q, ω) at all temperatures, explicitly yielding the elementary excitation spectrum.

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Exact solutions for Ising-model odd-number correlations on planar lattices

Cited by 52 publications

References 24 publications

Phase diagrams of the mixed spin-1 and spin-1/2 Ising–Heisenberg model on the diamond-like decorated Bethe lattice

Phase diagrams of the mixed spin-1 and spin-1/2 Ising–Heisenberg model on the diamond-like decorated Bethe lattice

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

Exact Solutions in a Spatially Anisotropic Quantum Spin Ladder Model Having Two- And Four-Spin Exchange Interactions

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