Papers by Keyword: Square Lattice

Abstract: We studied magnetic orderings and frustrations on 1D chain and 2D lattices: square, triangular, kagome, and hexagonal in the Ising, 3-state Potts and standard 4-state Potts models. The spins interrelate with one another via the nearest-neighbor, the next-nearest-neighbor or the third-neighbor exchange interactions and by an external magnetic field. For problem solving we mainly calculated the entropy and specific heat using the rigorous analytical solutions for maximum eigenvalue of Kramers-Wannier transfer-matrix and exploiting computer simulation, par excellence, by Wang-Landau algorithm. Whether a system is ordered or frustrated is related to the signs and values of exchange interactions. An external magnetic field may both favor the ordering of a system and create frustrations. With the help of calculations of the entropy, the specific heat and magnetic parameters, we obtained the points and ranges of frustrations, the frustration fields and the phase transition points. The results obtained also show that the same exchange interactions my either be competing or noncompeting which depends on the topology of a lattice.

Abstract: Looking for photonic crystals with wide absolute bandgaps is always a challenging, attractive and significant task for optics scientists and optics engineers. In this paper, a new square-lattice photonic crystal structure is proposed based on a unit cell with a hollow cylinder and cross connecting plates. It is demonstrated through plane wave expansion method to have wider absolute photonic bandgaps compared with others reported.

Abstract: In this paper, a new structure of two-dimensional (2D) square-lattice photonic crystal (SLPC) with button-shaped dielectric rods (BSDRs) is designed, and the properties of band gaps are analyzed by Plane Wave Expansion Method (PWM). The optimal samples that possess the width of absolute band gap are obtained by scanning the three parameters: the radius of large circular R in button mark, the ratio of the radius of small circular to the radius of large circular r/R, and the rotating angle of button mark Ө. It is shown that when r/R=0.485, R=0.406um, and Ө =75⁰, the largest absolute band gap of 0.0406 (ωa/2πc) exists for normalized frequencies in the range 0.7501 to 0.7910 (ωa/2πc). Besides，we can get at most five absolute band gaps when r/R=0.485, R=0.406um, and Ө =60⁰.

Abstract: Based on the assumption that sp3 hybridization is more stable in bulk silicon, this study is a step forward in understanding the structures and mechanical properties of silicon nanotubes (SiNT). Using the well tested form of Tersoff potential we have calculated cohesive energy and other parameters for SiNT of various diameters and chiralities. Using this potential, the results obtained for bulk silicon are satisfactory, so we expect that the same potential would work well with SiNT as well. We calculated Young’ modulus and shear modulus for SiNT. Young’s modulus lies in the range of 100- 200 GPa which is about 10-20 times lower than CNT and shear modulus lies between 200-300 GPa. This work shall motivate further theoretical and experimental work in the field of nanostructures.