Nearest-neighbor exchange interaction

Thence next-nearest neighbor exchange interactions appear, as well as modifications to the nearest-neighbor interactions. Additional structure-dependent modifications to the nearest-neighbor interactions occur if the e(i x j) and e(y x k) parameters are distinguished. Such modifications we pass over here and use simply a second-order nearest-neighbor interaction parameter... 

Fig. 7.40. Magnon dispersion in ErFej along <110) and (111) symmetry directions. The squares denote points measured on the lower optic branch the circles denote points on the acoustic and upper optic branches. The solid line is the result of the nearest neighbor exchange interaction fitting calculation described in the text (after Rhyne et al., 1976).

The transverse-field Ising model is defined on a d-dimensional hypercubic (i.e., square, cubic, etc.) lattice. Each site is occupied by a quantum spin-. The spins interact via a ferromagnetic nearest-neighbor exchange interaction / > 0 between their z components. The transverse magnetic field couples to the x components of the spins. The Hamiltonian of the model is given by... 

Figure 9 First nearest-neighbor exchange interaction of X in the ferromagnetic state y = 0.0 (filled circles), y triangles). The lines serve as a guide for eye.

The data above Tsp cannot be described with a uniform chain model, but can be explained by including the existence of a next-nearest interaction 2Jtam/k = — 58 K to the presence of a nearest neighbor exchange 2J/k = -160 K. ... 

J, i A- nearest (A) and next nearest (A) neighbor exchange interaction energies... 

In Fig. 12 we present some results of MFKEbbased simulation of spinodal decomposition with the vacancy-mediated exchange mechanism. We use the same 2D model on a square lattice with the nearest-neighbor interaction and Fp = 0 as in Refs., ... 

Exchange interactions only occur if the donor and acceptor ions are close enough for direct overlap of their electronic wavefunctions. Consequently, energy transfer due to quantum mechanical exchange interactions between the D and A ions is only important at very short distances (nearest neighbor positions). In fact, the transfer probability varies similarly to the overlap of the wavefunctions Pt a where... 

Figure 2. The nearest-neighbor concurrence C(l,2) for different values of the anisotropy parameter y = 1, 0.7, 0.3, 0 with an impurity located at = 3 as a function of the reduced coupling constant A = 7/2/i, where J is the exchange interaction constant and h is the strength of the external magnetic field. The curves correspond to different values of the impurity strength a = 0,0.5,1,1.5 with system size iV = 201.

We consider a simple cubic lattice with a coordination number 2 = 6. For an incompressible polymer solution, each lattice site is occupied by a solvent molecule or by a segment of polymer chain. The attraction interactions between the nearest-neighbor sites are characterized by a reduced exchange energy = fi( pp + ss 2eps) between a segment p and a solvent s, where is the attractive energy of an i—j pair. 

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