Approaches to numerical solution of 2D Ising model

Soldatov, Konstantin; Nefedev, Konstantin; Kapitan, Vitalii; Andriushchenko, Petr

doi:10.1088/1742-6596/741/1/012199

Cited by 6 publications

(2 citation statements)

References 8 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…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

View full text Add to dashboard Cite

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.

show abstract

Section: Introductionmentioning

confidence: 99%

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

et al. 2021

View full text Add to dashboard Cite

show abstract

“…In condensed matter physics is increase of the influence of computer simulation, which allows the development of new methods for the construction of complex nanostructures and which promotes the discovery of new phenomena and materials [5][6][7][8][9][10][11][12][13]. The study of collective behavior of magnetic systems will allow to predict and manage the properties of new materials, and will also make a significant contribution to the development of fundamental knowledge about the nano-world and ongoing processes.…”

Section: Introductionmentioning

confidence: 99%