Magnetic properties of an Ising ladder-like graphene nanoribbon by using Monte Carlo method

Yang, Min; Wang, Wei; Li, Bo-chen; Wu, Hao-Jia; Yang, Shao-qing; Yang, Jun

doi:10.1016/j.physa.2019.122932

Cited by 57 publications

(17 citation statements)

References 87 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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“…In previous works, 30‐34 the multiferroics properties of the mixed spin Ising model are investigated. The Hamiltonian of thin films BiFeO 3 is given by

H = - j_{1} \sum_{< i, j >} p_{i} p_{j} - j_{2} \sum_{< i, j >} p_{i} p_{j} - E \sum_{i} p_{i}

with j 1 (Bi 3+ ‐Bi 3+ ) and j 2 (Bi 3+ ‐Bi 3+ ) are the ferroelectric couplings between the first and second nearest neighbors in thin films BiFeO 3 .…”

Section: Methodsmentioning

confidence: 99%

Ferroelectric, quantum efficiency and photovoltaic properties in perovskite BiFeO ₃ thin films: First principle calculations and Monte Carlo study

2021

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Summary Monte Carlo simulations and the full‐potential linearized augmented plane wave (FP‐LAPW) method in the framework of density functional theory (DFT) are applied to investigate the quantum efficiency, ferroelectric, and photovoltaic properties. We have used the generalized Perdew Burke Ernzerhof gradient approximation (PBE‐GGA) as well as the Becke‐Johnson modified exchange potential (TB‐mBJ) to correct the gap's energy. The gap energy results of 2.5 eV obtained using mBJ are reasonable compared to the available experimental data (2.5 eV). The difference energy ∆E between the magnetic configurations EFM and EAFM of Fe was calculated. The BiFeO3 possesses the insulating ground state and G‐type antiferromagnetic ordering. The value of the magnetic moment was compared with the values obtained using experience and theory. The quantum efficiency (EQE), the short‐circuit current and open circuit voltage are investigated using ab‐initio calculations. The polarization, dielectric susceptibility and hysteresis loops are investigated using the Monte Carlo simulations for several thin films of BiFeO3.

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“…From a physical point of view, Q exists under the competition between temperature, exchange interaction and magnetic field, and the larger Jcd is more dominant in the competition among the three. It can bind the spin to a fixed state which is not easy to change, thus leading to the stability and invariability of Q [33][34][35][36][37][38]41]. In Fig.…”

Section: Dynamic Order Parameter Susceptibility Internal Energy Anmentioning

confidence: 99%

“…In our previous works, much effort was made on the magnetic and dielectric properties of the low-dimensional mixed-spin nano-systems using Monte Carlo simulations [33][34][35][36][37][38]. In addition, such BiFeO3/FM bilayer system was also investigated [39][40][41].…”

Section: Introductionmentioning

confidence: 99%

Insight into dynamic magnetic properties of YMnO3/FM bilayer in a time-dependent magnetic field

Chang

Wang

et al. 2021

Preprint

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Based on the Monte Carlo simulation, a mixed-spin (5/2, 2, 3/2) Ising model is constructed to investigate the dynamic magnetic properties of antiferromagnetic/ferromagnetic YMnO 3 /FM bilayer under the existence of a time-dependent magnetic field. The effects of exchange interaction, oscillating magnetic field as well as temperature are involved in this work. Masses of numerical results of the dynamic order parameter, susceptibility, internal energy, and blocking temperature are obtained with diverse physical parameters. Moreover, the phase diagrams and the hysteresis loops of the system are discussed in detail as well for a better understanding of the dynamic properties of the present system.

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Magnetic properties of an Ising ladder-like graphene nanoribbon by using Monte Carlo method

Cited by 57 publications

References 87 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

Ferroelectric, quantum efficiency and photovoltaic properties in perovskite BiFeO ₃ thin films: First principle calculations and Monte Carlo study

Insight into dynamic magnetic properties of YMnO3/FM bilayer in a time-dependent magnetic field

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Magnetic properties of an Ising ladder-like graphene nanoribbon by using Monte Carlo method

Cited by 57 publications

References 87 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

Ferroelectric, quantum efficiency and photovoltaic properties in perovskite BiFeO 3 thin films: First principle calculations and Monte Carlo study

Insight into dynamic magnetic properties of YMnO3/FM bilayer in a time-dependent magnetic field

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Ferroelectric, quantum efficiency and photovoltaic properties in perovskite BiFeO ₃ thin films: First principle calculations and Monte Carlo study