Magnetic and thermodynamic characteristics of a rectangle Ising nanoribbon

Li, Qi; Li, Rundong; Wang, Wei; Geng, Rui-ze; Huang, Huey W.; Zheng, Shu-juan

doi:10.1016/j.physa.2020.124741

Cited by 41 publications

(18 citation statements)

References 67 publications

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“…Furthermore, Zhang's results agree with some experimental results, which are carefully performed with high accuracy (see in [31], for instance). After its publication [3], Zhang's conjectured solution has received supports from several groups, for instance, March and his co-workers [32][33][34][35][36], Ławrynowicz and some mathematicians [6,7,37,38], Kaupuzs and his colleagues [30,39,40], and others [41][42][43][44][45][46][47][48][49][50][51][52][53]. In [8], Zhang-Suzuki-March rigorously proved four Theorems, which verifies the correctness of the Zhang's conjectured solution [3].…”

Section: Introductionmentioning

confidence: 99%

A Method of Riemann–Hilbert Problem for Zhang’s Conjecture 1 in a Ferromagnetic 3D Ising Model: Trivialization of Topological Structure

Сузукі

Zhang

2021

Mathematics

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A method of the Riemann–Hilbert problem is applied for Zhang’s conjecture 1 proposed in Philo. Mag. 87 (2007) 5309 for a ferromagnetic three-dimensional (3D) Ising model in the zero external field and the solution to the Zhang’s conjecture 1 is constructed by use of the monoidal transform. At first, the knot structure of the ferromagnetic 3D Ising model in the zero external field is determined and the non-local behavior of the ferromagnetic 3D Ising model can be described by the non-trivial knot structure. A representation from the knot space to the Clifford algebra of exponential type is constructed, and the partition function of the ferromagnetic 3D Ising model in the zero external field can be obtained by this representation (Theorem I). After a realization of the knots on a Riemann surface of hyperelliptic type, the monodromy representation is realized from the representation. The Riemann–Hilbert problem is formulated and the solution is obtained (Theorem II). Finally, the monoidal transformation is introduced for the solution and the trivialization of the representation is constructed (Theorem III). By this, we can obtain the desired solution to the Zhang’s conjecture 1 (Main Theorem). The present work not only proves the Zhang’s conjecture 1, but also shows that the 3D Ising model is a good platform for studying in deep the mathematical structure of a physical many-body interacting spin system and the connections between algebra, topology, and geometry.

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Section: Introductionmentioning

confidence: 99%

A Method of Riemann–Hilbert Problem for Zhang’s Conjecture 1 in a Ferromagnetic 3D Ising Model: Trivialization of Topological Structure

Сузукі

Zhang

2021

Mathematics

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“…[1][2][3][4][5][6] The variety of magnetic structures and spins combinations that have been analyzed by these mixed Ising models is quite wide. Some examples are as follows: nanostructures such as nanographene layers alternated with spins 1/2, 3/2, and 5/2 that have compensation points in the presence of an external magnetic field, [7,8] cluster dendrimers (CD) of core/shell (CDCS) with the (3/2-2) spin mixture, and a mixed spin-(2-3/2) Heisenberg single-walled nanotube superlattice, [9,10] Ising nanoribbons, [11] Ising nanocubes, [12] Ising nanowires, [13,14] and nanoislands. [15] The dynamical behavior of these mixed Ising structures in the presence of oscillating magnetic fields has been the object of many recent studies, particularly the dynamical hysteresis loops [16][17][18] and the dynamical compensation temperatures.…”

Section: Introductionmentioning

confidence: 99%

Mixed Spin‐(3/2,7/2) Ising‐Type Ferrimagnet: Monte Carlo–Mean Field Treatment

Espriella

Karimou

Buendı́a

2021

Physica Status Solidi (b)

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Mean field and Monte Carlo simulations techniques are applied to study the behavior of a mixed Ising spin model in a square lattice where spins 7/2 are located in alternating sites with spins 3/2. There is an antiferromagnetic interaction between nearest neighbors, ferromagnetic interactions between next-nearest neighbors, crystal fields, and a magnetic external field. The role of the different interactions in the magnetic behavior of the system is explored. It is found that depending on the combination of parameters in the Hamiltonian this system presents multiple hysteresis loops, exchange bias, compensation temperatures, and discontinuous magnetizations. The results are compared with previous studies that do not include the ferromagnetic next-nearest neighbor interactions and found that they can have a strong effect in the magnetic behavior of the system.

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“…Various studies emphasize the effect of temperature, magnetic field, exchange coupling, and crystal field on the magnetic properties of the system [16][17][18]. Many shaped structures have been studied such as hexagonal core-shell [19][20][21], ladderlike boronene nanoribbon [22], square-octagon lattice [23], Blume-Capel system for square and simple cubic lattices [24][25][26], borophene core-shell structure [27], ladder-like graphene nanoribbon [28][29][30][31], triangular lattice [31,32], diamond-like decorated square [33], rectangle Ising nanoribbon [34].…”

Section: Introductionmentioning

confidence: 99%

Compensation and transition order temperature behavior of mixed spin-1 and spin-1/2 ising model on a centered honeycomb-hexagonal structure: two points of compensation

2022

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The magnetic properties and phase diagrams of the mixed spin-1/2 and spin-1 Ising model on a honeycomb inside a hexagonal structure have been studied using the Monte Carlo simulations based on the Metropolis update protocol. The effect of different exchange interactions (intralayer and interlayer Js') and single-ion anisotropy D on the magnetic properties, transition and compensation temperatures, and magnetic susceptibility have been investigated. The phase diagrams, T-J and T-D, for different exchange interactions and crystal field values have been examined. Compensation behavior exists for critical values of interlayer's exchange interactions. Our calculations reveal the existence of two points of compensation for a narrow range of negative D. Article highlights A mixed spin Ising model on a centered honeycomb-hexagonal structure was proposed The effects of crystal field and exchange coupling were studied Two points of compensation temperature were exist.

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Magnetic and thermodynamic characteristics of a rectangle Ising nanoribbon

Cited by 41 publications

References 67 publications

A Method of Riemann–Hilbert Problem for Zhang’s Conjecture 1 in a Ferromagnetic 3D Ising Model: Trivialization of Topological Structure

A Method of Riemann–Hilbert Problem for Zhang’s Conjecture 1 in a Ferromagnetic 3D Ising Model: Trivialization of Topological Structure

Mixed Spin‐(3/2,7/2) Ising‐Type Ferrimagnet: Monte Carlo–Mean Field Treatment

Compensation and transition order temperature behavior of mixed spin-1 and spin-1/2 ising model on a centered honeycomb-hexagonal structure: two points of compensation

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