An investigation of the modern phenomena of condensed matter physics, called, magnetization plateau and magnetization jump, visible as anomalies in spin susceptibility at zero temperature, have been carried out theoretically in a zero-dimensional Boron Triangular Kagome Lattice (0D-BTKL), namely quantum dots of BTKL, subjected to a staggering subLattice potential. By analyzing the Ruderman-Kittel-Kasuya-Yoshida (RKKY) interaction, the magnetic ground state of the 0D-TKL in the presence of two magnetic adatoms, in the presence of a staggered subLattice potential is evaluated. The important salient feature of the 0D-BTKLs is the emergence of the RKKY plateaus versus the Fermi energy. The spatial configurations of the magnetic impurities dramatically change the quality and quantity of the RKKY plateaus. These RKKY plateaus have not been reported before, to the best of our knowledge. Our finite-size results successfully confirm that both the width and location of the RKKY plateaus are tunable using an external potential and Fermi energy. Another remarkable observation is the nontrivial behavior, namely the magnetization jump, which accompanies the discontinuity in the spin susceptibility curves versus the staggering potential in our calculations. We believe that our results provide significant insights towards designing further experiments to search for the realization of the magnetization plateau phases and magnetization jumps in spintronics and pseudospin electronics devices based on BTKLs.

The Ising model is one of the simplest models describing the interacting particles. In this work, we calculate the high temperature series expansions of zero field susceptibility of ising model with ferromagnetic, antiferromagnetic and one antiferromagnetic interactions on two dimensional Kagome Lattice. Using the Pade´ approximation, we calculate the susceptibility of critical exponent of ferromagnetic ising model  g » 1.75, which is consistent with universality hypothesis. However, antiferromagnetic and one antiferromagnetic interaction ising model doesn’t show any transition at finite temperature because of the effect of magnetic frustration.

Investigation of broken symmetry phases with long range order in strongly correlated electron systems is among subjects that have always been of interest to condensed matter scientists. In this paper we tried to study the existence of the 120 degrees magnetic spiral order, based on anisotropy in geometrically frustrated Triangular Lattices, using variational cluster approximation. We observed that by increasing the anisotropy in the system, the spiral order can be found for AWT IMAGE and for AWT IMAGE; however, it is limited by decreasing AWT IMAGE since antiferromagnetism is dominant for AWT IMAGE. Studying the Mott transition shows that a paramagnetic insulating phase, called quantum spin liquid, happens in the neighborhood of the spiral ordered phase.

In this paper, some different statistical growth models have been simulated on regular (square, Triangular and hexagonal) and random (Voronoi) Lattices. It has been showed that design of substrate doesn’t affect the growth universal class, but only changes the roughness of the growth surface.

Thin sheets stiffened with Lattice structures are used widely in many engineering industries. Investigation of stability behavior for the grid structures and determination of the buckling load under compressive loads is an issue that has attracted the attention of many researchers, and extensive studies have been done in this field. In this paper, a new grid called Diacube is introduced and its buckling load is examined. For this aim, first, the buckling behavior of 5 common types of stiffened flat Lattice panels containing hexagonal, Triangular, square, diamond and Kagome grid are investigated under compressive axial load; and the results are compared with Diacube grid. The effect of network density used in each structure on the buckling of these structures is studied under different boundary conditions. Regarding the mass difference of samples, specific critical load parameter (the buckling load to mass ratio) is used for comparison between the structures. Using the finite element modeling and numerical analysis, the grid that has the highest buckling load in each boundary condition is determined. It is found that if unloaded edges in Lattice panels are simply supported, the new Diacube grid will have the highest buckling load among all structures. Finally, validity of the numerical result obtained for two samples of the structures including hexagonal and Diacube grid is evaluated experimentally; and the numerical results are confirmed.

Topological indices are numerical parameters of a graph which characterize its topology and are usually graph invariant. In QSAR/QSPR study, physico-chemical properties and topological indices such as Randic, atom-bond connectivity (ABC) and geometric-arithmetic (GA) index are used to predict the bioactivity of chemical compounds. Graph theory has found a considerable use in this area of research.In this paper, we study and derive analytical closed results of general Randic index R_α (G) for Boron Triangular sheet BTS(m,n), Borophene chain of B_36 (n) and Melem chain MC(n). We also compute the general first Zagreb, ABC, GA, ABC 4 and GA 5 indices for sheet and chains for the first time and give closed formulas of these degree based indices.

Triangular norms in the study of probabilistic metric spaces as a special kind of associative functions defined on the unit interval. These functions have found applications in many areas since then. In this study, we present new methods for constructing Triangular norms and Triangular conorms on an arbitrary bounded Lattice under some constraints. Also, we give some illustrative examples for the clarity. Finally, we show that our construction methods can be generalized by induction to a modified ordinal sum for Triangular norms and Triangular conorms on an arbitrary bounded Lattice, respectively.

As a proper generalization of the ordinal sum t-norm construction on bounded Lattices proposed in [E. A\c{s}{\i}c{\i}, R. Mesiar, New constructions of Triangular norms and Triangular conorms on an arbitrary bounded Lattice, International Journal of General Systems, {\bf 49}(2) (2020), 143-160], the present paper studies a new extension of a Triangular norm on a subinterval $[0,\alpha]$ via an interior operator to the underlying entire bounded Lattice, where the necessary and sufficient conditions under which the constructed operation is again a t-norm are given. By comparing the graphic structures of two t-norms on a common bounded Lattice which are constructed in different ways, it is shown that the new method in this paper is essentially different from the ones existing in the literature. As an end, this new construction is generalized to construct ordinal sums of finitely many t-norms by recursion on bounded Lattices. The dual results for ordinal sum construction of t-conorms via closure operators on bounded Lattices are also presented.

Over the past years, two-dimensional materials such as graphene, phosphorene, silicene, and Boron-nitride have attracted the attention of many researchers. After the successful synthesis of graphene, due to its many new applications, researches began to produce nanosheets from other elements, and among these elements, Boron was one of the options. In the periodic table of elements, Boron is ahead of carbon and after beryllium, which exhibits metallic and non-metallic properties. The two-dimensional Boron sheets called borophene are one of the allotropes of this element that reaches their stable and single-layer structure by forming Triangular Lattice and the carbon like SP 2 hybridization. Since Boron is carbon’ s neighbour, so it is expected that two-dimensional Boron sheets would have properties close to graphene. Here, we investigate the wettability of the borophene mono-layer surface by calculating contact angle of the water and the surface of the sheet by using the molecular dynamics simulation method. According to the measurements obtained from this simulation, the contact angle is approximately 131 degrees, indicating that such a structure is hydrophobic. Also, the effect of diameter of nanodroplet on the surface contact angle has been studied. Keywords: wettability, borophene,