Simulation of an extended 3D mixed Ising model by Monte Carlo method

Ferromagnetic vanadium disulfide VS2monolayers with high Curie temperature and high spin polarization

“…It is worth noting that the simple 2D Ising model can hardly meet our exploration of the magnetic and thermal properties of complex systems. Therefore, we here use the extended 2D Ising model 35–39 to conduct relevant simulations. In this framework, the Hamiltonian of the VS 2 monolayer can be expressed as: , where J represents the nearest-neighboring exchange coupling in the layer, D represents the crystal field for sublattice V, and h is the external longitudinal magnetic field.…”

“…It is worth noting that the simple 2D Ising model can hardly meet our exploration of the magnetic and thermal properties of complex systems. Therefore, we here use the extended 2D Ising model [35][36][37][38][39] to conduct relevant simulations. In this framework, the Hamiltonian of the VS 2 monolayer can be expressed as:…”

Sampling methods for solving Bayesian model updating problems: A tutorial

“…For simplicity, the comparison between frequencies f 1 and f 4 , and between frequencies f 6 and f 7 are in Figs. [28][29][30] in Section A.2 show the scatter plot profile comparison for all frequencies.…”

“…The uncertainty in the model parameters h can be accounted for by using a probability density function. By doing so, the modeller can construct a stochastic model (or a class of models [14])) to predict probabilistically the possible values of the system output D, and therefore its statistics, given the vector of uncertain model parameters h. These are the so-called forward problems which can be solved by means of analytical approaches [25][26][27] or in general by Monte Carlo simulation approaches [28][29][30]. In the latter approach, the statistics of D are obtained by first generating n realisations of the h k (for k ¼ 1; .…”

Electronic structure and magnetothermal properties of two-dimensional ScCl

“…50 Considering the structural characteristics of monolayer ScCl, the 2D periodic boundary conditions were adopted and 1 × 10 6 iterations were calculated for each spin flip in a 30 × 30 × 1 supercell. In addition, based on the 2D Ising model, 51–54 the Hamiltonian of monolayer ScCl can be expressed as follows: where J represents the exchange coupling between the nearest magnetic atoms (Sc), D represents the magnetocrystalline anisotropy of the monolayer ScCl, and h represents the longitudinal magnetic field intensity exerted on the system. S z i in the formula represents the spin value projection of the i th magnetic atom along the z direction, where the projected values are discrete ( S z i = ±1/2).…”