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Frustrations in the Ising chain with the third-neighbor interactions

Alexander V. Zarubin, Felix A. Kassan-Ogly, Alexey I. Proshkin

arXiv:2002.05430Journal of Magnetism and Magnetic MaterialsJun 20, 202010 citations

Frustrations and orderings in Ising chain with multiple interactions

Alexander V. Zarubin, Felix A. Kassan-Ogly, Alexey I. Proshkin

Abstract The frustration properties of the Ising model on a one-dimensional monoatomic equidistant lattice are investigated taking into account the exchange interactions of atomic spins at the sites of the first (nearest), second (next-nearest) and third neighbors. The exact solution of the model was obtained using the Kramers–Wannier transfer matrix method. The types of magnetic ordering of the ground state of the model are determined, and a magnetic phase diagram is constructed. Criteria are formulated for the occurrence of magnetic frustrations in the presence of competition between the energies of exchange interactions. Non-zero entropy values in the ground state of the frustrated system were found.Abstract The frustration properties of the Ising model on a one-dimensional monoatomic equidistant lattice are investigated taking into account the exchange interactions of atomic spins at the sites of the first (nearest), second (next-nearest) and third neighbors. The exact solution of the model was obtained using the Kramers–Wannier transfer matrix method. The types of magnetic ordering of the ground state of the model are determined, and a magnetic phase diagram is constructed. Criteria are formulated for the occurrence of magnetic frustrations in the presence of competition between the energies of exchange interactions. Non-zero entropy values in the ground state of the frustrated system were found.

arXiv:2206.09177Journal of Physics Conference SeriesNov 1, 20194 citations

Geometric frustration in Ising diamond chains

J. S. Valverde, Onofre Rojas, S. M. de Souza

Physica A Statistical Mechanics and its ApplicationsDec 10, 200710 citations

Exact results for a generalized spin‐1/2 Ising–Heisenberg diamond chain with the second‐neighbor interaction between nodal spins

Bohdan Lisnyi, Jozef Strečka

The ground state and thermodynamics of a generalized spin‐1/2 Ising–Heisenberg diamond chain with the second‐neighbor interaction between nodal spins are calculated exactly using the mapping method based on the decoration–iteration transformation. Rigorous results for the magnetization, susceptibility, and heat capacity are investigated in dependence on temperature and magnetic field for the frustrated diamond spin chain with the antiferromagnetic Ising and Heisenberg interactions. It is demonstrated that the second‐neighbor interaction between nodal spins gives rise to a greater diversity of low‐temperature magnetization curves, which may include an intermediate plateau at two‐third of the saturation magnetization related to the classical ferrimagnetic (up–up–up–down–up–up– ) ground state with translationally broken symmetry besides an intermediate one‐third magnetization plateau reflecting the translationally invariant quantum ferrimagnetic (monomer–dimer) spin arrangement.The ground state and thermodynamics of a generalized spin‐1/2 Ising–Heisenberg diamond chain with the second‐neighbor interaction between nodal spins are calculated exactly using the mapping method based on the decoration–iteration transformation. Rigorous results for the magnetization, susceptibility, and heat capacity are investigated in dependence on temperature and magnetic field for the frustrated diamond spin chain with the antiferromagnetic Ising and Heisenberg interactions. It is demonstrated that the second‐neighbor interaction between nodal spins gives rise to a greater diversity of low‐temperature magnetization curves, which may include an intermediate plateau at two‐third of the saturation magnetization related to the classical ferrimagnetic (up–up–up–down–up–up– ) ground state with translationally broken symmetry besides an intermediate one‐third magnetization plateau reflecting the translationally invariant quantum ferrimagnetic (monomer–dimer) spin arrangement.

arXiv:1312.3439physica status solidi (b)Apr 3, 201427 citations

Ground state of the spin-1/2 Ising–Heisenberg distorted diamond chain with ferromagnetic Ising and antiferromagnetic Heisenberg interactions

Bohdan Lisnyi

The ground state of the spin-1/2 Ising–Heisenberg distorted diamond chain in the presence of an external magnetic field is investigated in the case of the ferromagnetic Ising and antiferromagnetic XXZ Heisenberg interactions, that exhibits a geometric frustration of spins. The influence of the quantum fluctuations, the magnetic field, and the distortion on the ground state are studied in detail. It is established that the zero-temperature magnetization curve may show intermediate plateaus at zero and one-third of the saturation magnetization.The ground state of the spin-1/2 Ising–Heisenberg distorted diamond chain in the presence of an external magnetic field is investigated in the case of the ferromagnetic Ising and antiferromagnetic XXZ Heisenberg interactions, that exhibits a geometric frustration of spins. The influence of the quantum fluctuations, the magnetic field, and the distortion on the ground state are studied in detail. It is established that the zero-temperature magnetization curve may show intermediate plateaus at zero and one-third of the saturation magnetization.

Low Temperature PhysicsJul 1, 20240 citations

Competing and aperiodic interactions in the Ising chain

Roberto F. S. Andrade, Silvio R. A. Salinas

Physica A Statistical Mechanics and its ApplicationsAug 1, 19970 citations

Frustration and ordering in Ising chain in an external magnetic field with third-neighbor interactions

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