On the Numerical Calculation of Frustrations in the Ising Model

Makarov, Aleksandr; Makarova, Kseniia; Shevchenko, Yu. A.; Andriushchenko, Petr; Kapitan, Vitalii; Soldatov, Konstantin; Perzhu, Alexander; Rybin, Alexey; Kapitan, Dmitrii; Васильев, Е. В.; Chubov, Yu. V.; Nefedev, Konstantin

doi:10.1134/s0021364019220090

Cited by 12 publications

(10 citation statements)

References 24 publications

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“…(15) is replaced by the "representative frequency" which somewhat deviates from the binding energy. The procedures outlined above have been effectively applied to excitons in bulk semiconductors [42][43][44] and have been recently www.advancedsciencenews.com www.pss-b.com applied to various TMDC monolayers [17,19,46] with reasonable agreement with experimental data. However, as already mentioned, such an approach (and even direct numerical solution of Eq.…”

Section: Dynamic Screening Of Excitonic Statesmentioning

confidence: 92%

“…In order to find the binding energies it is sufficient to determine the poles of Γ or of χ as a function of Ω; i.e., the energies hΩ where Γ becomes infinite. In this case, the first term in Figure 4a, can be omitted, and the Bethe-Salpeter equation for the exciton at rest (center of mass momentum is zero) takes the form [19,39,[41][42][43][44][45]…”

Section: Dynamic Screening Of Excitonic Statesmentioning

confidence: 99%

“…and solving the generalized Schrödinger Equation (11) with V eff q dependent on the eigenvalue E B , [17,42] see also Scharf et al [19] In the more advanced approach of Zimmermann, [43] the E B in the right hand side of Eq. (15) is replaced by the "representative frequency" which somewhat deviates from the binding energy.…”

Section: Dynamic Screening Of Excitonic Statesmentioning

confidence: 99%

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Breakdown of the Static Approximation for Free Carrier Screening of Excitons in Monolayer Semiconductors

Glazov

Chernikov

2018

Physica Status Solidi (b)

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The authors address the problem of free carrier screening of exciton states in two‐dimensional monolayer semiconductors. Basic theoretical considerations are presented concerning the applicability of the commonly used static approximation of the screening effect and the implications are discussed. The authors show that the low‐frequency models leads to a major overestimation of the free carrier response and are inadequate to describe the screening of strongly bound excitons in monolayer materials. The presented arguments are consistent with existing high‐level many‐body theories and transparently illustrate the underlying physics.

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Section: Dynamic Screening Of Excitonic Statesmentioning

confidence: 92%

Section: Dynamic Screening Of Excitonic Statesmentioning

confidence: 99%

Section: Dynamic Screening Of Excitonic Statesmentioning

confidence: 99%

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Breakdown of the Static Approximation for Free Carrier Screening of Excitons in Monolayer Semiconductors

Glazov

Chernikov

2018

Physica Status Solidi (b)

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“…It is impossible to realize antiferromagnetic order over the entire triangle-at least two spins are ordered ferromagnetically and at least one connection will be inevitably frustrated. Understanding the physics of frustrations is essential to understanding the properties of many materials such as spin and macrospin glasses [2,3], water ice [4,5], spin ice and artificial spin ice [6][7][8][9][10][11][12][13][14][15][16][17][18], and many others.…”

Section: Introductionmentioning

confidence: 99%

“…There are many approaches to obtaining an approximate solution of the Ising model; see, for example, [17,30,[45][46][47][48][49]. The exact calculation of the ground-state energy even for a classical Ising spin glass on a 2D lattice with the nearestneighbor interaction is a computationally difficult problem, or even NP-complete [41].…”

Section: Introductionmentioning

confidence: 99%

Low-energy states, ground states, and variable frustrations of the finite-size dipolar Cairo lattices

et al. 2021

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To investigate the influence of geometric frustration on the properties of low-energy configurations of systems of ferromagnetic nanoislands located on the edges of the Cairo lattice, the model of interacting Ising-like magnetic dipoles is used. By the method of complete enumeration, the densities of states of the Cairo pentagonal lattices of a finite number of Ising-like point dipoles are calculated. The calculated ground and low-energy states for systems with a small number of dipoles can be used to solve the problem of searching for the ground states in a system with a relatively large number of dipoles. It is shown that the ground-state energy of the Cairo pentagonal lattices exhibits nonmonotonic behavior on one of the lattice parameters. The lattice parameters can be used to control the degree of geometric frustration. For the studied lattices of a finite number of Ising dipoles on the Cairo lattice in the ground-state configurations, a number of closed pentagons is observed, which are different from the obtained maximum closed pentagons. The magnetic order in the ground-state configurations obeys the ice rule and the quasi-ice rules.

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