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Graphene-like quantum dots (GQDs) doped with magnetic ions are described in accordance with the mixed Ising model. The magnetic properties of this system are discussed within the framework of the effective field theory with correlations. The numerical results produced several types of phase diagrams with different exchange couplings and anisotropies. Certain unique features, such as reentrant phenomena, were found within a particular range of parameters. We concluded that GQDs doped with magnetic ions have the potential to adjust their performance and effectively enlarge the scope of application.

Three sizes of center decorated tetragonal nanoparticles are described by the transverse Ising model with the anisotropy. The phase diagram, the magnetization and the magnetic susceptibility for different sizes nanoparticles are studied within the effective field theory with correlations. The results show the size and anisotropy have different effects on the system, such as the reentrant on phase diagram and depressed saturation magnetization.

The magnetic properties of borophene structure are studied for the first time by the effective-field theory with correlations. This method has been successfully used in analyzing the magnetic mechanism of graphene. The borophene consisting of 36 boron atoms with a central hexagonal vacancy can be described by Ising model . The general formula of the magnetization for the borophene is given. Possible physical mechanism of the emergence magnetic properties is demonstrated. The effects of the exchange coupling and the anisotropy of the magnetization, the susceptibility the blocking temperature and hysteresis loops of borophene are discussed. We also illustrate the possibility to test the predicted magnetism in an experiment, such as the maximum on the magnetization curve. Our study may provide an opportunity for the design of a new type of memory-switching or sensors by using earth-rich nonmagnetic boron materials.

Magnetic properties of decorated 2D kagome-like lattice described by Ising model were studied by effective-field theory with correlations. Multiple hysteresis loops and possible situations for depressed saturation magnetizations were found within a range of parameters. A particular magnetization curve suddenly falling to zero corresponds to a first-order phase transition. In addition, phase diagrams of the decorated 2D kagome-like lattice were discussed.

We study two coupled cavities system, each of cavity containing a single two-level atom. Quantum entanglemt, quantum discord and quantum phase transition under ground state have been investigated. Atomic excitation number variance has used to characterize the quantum phase transition. We conclude that, in our model, quantum discord have nonzero values while quantum entanglement vanish and quantum discord is a more proper measure to characterize quantum transition.

Kekulene-like nanostructure is described by Ising model with anisotropy. Effective field theory with correlations is employed to study phase diagrams and magnetization of the system. The numerical results show the physical parameters, such as anisotropy and exchange couplings, have important effects on magnetic properties. Various types of phase diagrams and reentrant phase transition exhibit, which are sensitive of anisotropy and exchange coupling. Studying the phase transition of this structure could help to further understand new kekulene-like family.

The magnetic properties of a mixed spin-3/2 and spin-2 and a mixed spin-3/2 and spin-5/2 Ising ferromagnetic system with different anisotropies are studied by means of mean-field theory (MFT). The dependence of the phase diagram on single-ion anisotropy strengths is studied too. In the mixed spin-3/2 and spin-2 Ising model, besides the second-order phase transition, the first order-disorder phase transition and the tricritical line are found. In the mixed spin-3/2 and spin-5/2 Ising model, there is no first-order transition and tricritical line.