Unique magnetism in different sizes of center decorated tetragonal nanoparticles with the anisotropy

Lu, Zhao-Ming; Si, Nan; Wang, Yaning; Zhang, Fan; Meng, Jing; Miao, Hailing; Jiang, Wei

doi:10.1016/j.physa.2019.02.013

Cited by 33 publications

(3 citation statements)

References 46 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…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

View full text Add to dashboard Cite

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.

show abstract

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

View full text Add to dashboard Cite

show abstract

“…Although the magnetic properties of many nanosystems were investigated using effective field theory, a small number of studies were reported on the magnetic properties of nanographene systems were investigated by using effective field theory in the literature [64][65][66][67][68][69][70][71]. However, local spin orientation effects on the magnetizations of the monolayer nanographene (MLNG) have not been studied yet for ӨCTA=1300.…”

Section: Introductionmentioning

confidence: 99%

Local Spin Induced Magnetism In The Monolayer Nanographene

Yıldız

2019

Cumhuriyet Science Journal

View full text Add to dashboard Cite

In this paper, we investigated local spin orientation (up or down) effects on magnetizations of the monolayer nanographene by using effective field theory developed by Kaneyoshi. It is found that the monolayer nanographene and its components have very small magnetization (mC1≈mC2≈mC3≈mMLNG≈2.31x10-18≈0) at T≈0.00 for the Jd1<0 (C1-spin up, C2-spin down and C3-spin up). On the other hand, for Jd2<0, Jd3<0, Jd4<0, and Jd5<0, the monolayer nanographene and its components (C1, C2 and C3 atoms) have very large local spin induced magnetization (mC1≈mC2≈mC3≈mMLNG≈1;1>>2.31x10-18) than those of the Jd1<0. These results clearly indicate that the local spin orientation in the monolayer nanographene has very strong effect on its magnetism.

show abstract

“…In order to figure out the magnetic behavior of the spin-1/2 Heisenberg chains in terms of applied magnetic field and/or exchange couplings between spins, magnetization plateaus have considerably been examined for various copper oxide compounds [18,20,28,29,[35][36][37][38]. The behavior of uniform magnetization in the different phases with their dependence on the longitudinal (transverse) field for fixed values of other applied parameters was studied by P. Thakur et al [1].…”

Section: Introductionmentioning

confidence: 99%

Magnetic properties of an antiferromagnetic spin-1/2 XYZ model in the presence of different magnetic fields: finite-size effects of inhomogeneity property

Zad,

Zoshki,

Sabeti

2018

Preprint

View full text Add to dashboard Cite

Magnetic and thermodynamic properties of the anisotropic XYZ spin-1/2 finite chain under both homogeneous and inhomogeneous magnetic fields are theoretically studied at low temperature. Using exact diagonalization method (ED), we study the magnetization, magnetic susceptibility and specific heat of the model characterized in terms of the finite correlation length in the presence of three different magnetic fields including longitudinal, transverse and transverse staggered magnetic fields. The magnetization, susceptibility and the specific heat of the model are investigated under two conditions separately: I) when the model is putted in the presence of homogeneous magnetic fields; II) when finite inhomogeneities are considered for all applied magnetic fields in the Hamiltonian. We show that for the finite-size XYZ chains at low temperature, the evident magnetization plateaus gradually convert to their counterpart quasiplateaus when the transverse magnetic field increases. Moreover, the influence of the transverse and staggered transverse magnetic fields, and their corresponding inhomogeneities on the magnetization process, magnetic susceptibility, and specific heat are reported in detail. Our exact results illustrate that by altering the inhomogeneity parameters, magnetization plateaus gradually convert to their counterpart quasi-plateaus. The specific heat manifests Schottky-type maximum, double-peak and triple-peak, as well as, transformation between them by varying considered inhomogeneity parameters in the Hamiltonian.

show abstract

Unique magnetism in different sizes of center decorated tetragonal nanoparticles with the anisotropy

Cited by 33 publications

References 46 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

Local Spin Induced Magnetism In The Monolayer Nanographene

Magnetic properties of an antiferromagnetic spin-1/2 XYZ model in the presence of different magnetic fields: finite-size effects of inhomogeneity property

Contact Info

Product

Resources

About