Linear chain of classical spins with arbitrary isotropic nearest-neighbor interaction

1977 ◽  
Vol 16 (5) ◽  
pp. 2311-2312 ◽  
Author(s):  
J. D. Parsons
Keyword(s):  
Nearest Neighbor ◽  
Linear Chain ◽  
Neighbor Interaction

Magnetic Properties of the Random Mixture of the Classical Heisenberg Spins

1975 ◽  
Vol 53 (9) ◽  
pp. 854-860 ◽  
Author(s):  
Shigetoshi Katsura
Keyword(s):  
Critical Temperature ◽  
Nearest Neighbor ◽  
Linear Chain ◽  
Three Dimensional ◽  
Bethe Lattice ◽  
Zero Field ◽  
Qualitative Properties ◽  
Neighbor Interaction ◽  
Random Mixture ◽  
Ising Spins

The specific heat, the susceptibility, and the correlation function at zero field above the critical temperature of the random mixture (quenched site and bond problems) of the classical Heisenberg spins with nearest neighbor interaction were obtained exactly for the linear chain and for an infinite Bethe lattice (Bethe approximation of the two and three dimensional lattices) above the critical temperature. The results are simply expressed by the replacements of 2 cosh K → 4π (sinh K)/K and tanh K → L(K) (L(K) = Langevin function) for K = KAA, KAB, KBA, and KBB in the corresponding expressions of the random mixture of the Ising spins, and qualitative properties of both models are similar.

On Next‐Nearest‐Neighbor Interaction in Linear Chain. II

1969 ◽  
Vol 10 (8) ◽  
pp. 1399-1402 ◽  
Author(s):  
Chanchal K. Majumdar ◽  
Dipan K. Ghosh
Keyword(s):  
Nearest Neighbor ◽  
Linear Chain ◽  
Neighbor Interaction

On Next‐Nearest‐Neighbor Interaction in Linear Chain. I

1969 ◽  
Vol 10 (8) ◽  
pp. 1388-1398 ◽  
Author(s):  
Chanchal K. Majumdar ◽  
Dipan K. Ghosh
Keyword(s):  
Nearest Neighbor ◽  
Linear Chain ◽  
Neighbor Interaction

ABSENCE OF PHASE TRANSITIONS ON TREE STRUCTURES

1993 ◽  
Vol 07 (29n30) ◽  
pp. 1947-1950 ◽  
Author(s):  
RAFFAELLA BURIONI ◽  
DAVIDE CASSI
Keyword(s):  
Long Range ◽  
Nearest Neighbor ◽  
Linear Chain ◽  
Mean Field ◽  
Range Order ◽  
The Other ◽  
Long Range Order ◽  
Field Phase ◽  
Tree Structures ◽  
Bethe Lattices

We rigorously prove that the correlation functions of any statistical model having a compact transitive symmetry group and nearest-neighbor interactions on any tree structure are equal to the corresponding ones on a linear chain. The exponential decay of the latter implies the absence of long-range order on any tree. On the other hand, for trees with exponential growth such as Bethe lattices, one can show the existence of a particular kind of mean field phase transition without long-range order.

Integrable Multi-impurity Open XXZ Chain with Next-Nearest-Neighbor Interaction

1999 ◽  
Vol 16 (6) ◽  
pp. 434-436
Author(s):  
Yun-zhong Lai ◽  
Ai-zhen Zhang ◽  
Zhan-ning Hu ◽  
Jiu-qing Liang ◽  
Fu-ke Pu (Pu Fu-cho)
Keyword(s):  
Nearest Neighbor ◽  
Neighbor Interaction ◽  
Xxz Chain

Total Energy Differences Between Silicon Carbide Polytypes and their Implications for Crystal Growth

1997 ◽  
Vol 492 ◽  
Author(s):  
Sukit Llmpijumnong ◽  
Walter R. L. Lambrecht
Keyword(s):  
Silicon Carbide ◽  
Crystal Growth ◽  
Epitaxial Growth ◽  
Size Effects ◽  
Nearest Neighbor ◽  
Orbital Method ◽  
Full Potential ◽  
Neighbor Interaction ◽  
Island Size ◽  
Annni Model

ABSTRACTThe energy differences between various SiC polytypes are calculated using the full-potential linear muffin-tin orbital method and analyzed in terms of the anisotropie next nearest neighbor interaction (ANNNI) model. The fact that J1 + 2J2 < 0 with J1 > 0 implies that twin boundaries in otherwise cubic material are favorable unless twins occur as nearest neighbor layers. Contrary to some other recent calculations we find J1 > |J2|. We discuss the consequences of this for stabilization of cubic SiC in epitaxial growth, including considerations of the island size effects.

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