Two-dimensional Heisenberg antiferromagnet with next-nearest-neighbor coupling

1989 ◽  
Vol 39 (4) ◽  
pp. 2887-2889 ◽  
Author(s):  
J. E. Hirsch ◽  
S. Tang
Keyword(s):  
Nearest Neighbor ◽  
Two Dimensional ◽  
Heisenberg Antiferromagnet ◽  
Nearest Neighbor Coupling

Spin-1/2 Heisenberg antiferromagnet with anisotropic nearest- and next-nearest-neighbor coupling

1992 ◽  
Vol 46 (17) ◽  
pp. 11133-11136 ◽  
Author(s):  
William J. Massano ◽  
Janice D. Prie ◽  
Jay D. Mancini
Keyword(s):  
Nearest Neighbor ◽  
Heisenberg Antiferromagnet ◽  
Nearest Neighbor Coupling

Influence of Point Defects on Band Gaps of Fe-Epoxy in Two-Dimensional Phononic Crystal

2013 ◽  
Vol 652-654 ◽  
pp. 1377-1382
Author(s):  
Jiao He ◽  
Guang Hui Fan ◽  
De Xun Zhao ◽  
Ying Kai Liu
Keyword(s):  
Point Defect ◽  
Band Gap ◽  
Nearest Neighbor ◽  
Phononic Crystal ◽  
Expansion Method ◽  
Band Gaps ◽  
Two Dimensional ◽  
Defect States ◽  
Filling Fraction ◽  
Nearest Neighbor Coupling

The band gap of a new two-dimensional phononic crystal was studied by the plane-wave expansion method. The two-dimensional phononic crystal is formed by square-shape array geometry of iron cylinders with square cross section inserted in an epoxy resin. The band gaps of different structures were calculated such as defect-free, single cavity crystal point defect states, crystal point defect states with (10) direction coupling, crystal point defect states with (10) direction next-nearest-neighbor coupling, and crystal point defect states with (11) direction next-nearest-neighbor coupling. Compared with that of defect-free, it is conclude that point defect is beneficial to the production of band gaps. The bandwidth of point defect is about 5 times larger than that of the defect-free crystal with the filling fraction F=0.4. In addition, the maximum number of band gap is in the crystal point defect states with (10) direction next-nearest-neighbor coupling. It will provide a theoretical reference for the manufacture of phononic crystal.

Variational solution for the spin Heisenberg antiferromagnet with nearest and next nearest neighbor coupling

1992 ◽  
Vol 84 (6) ◽  
pp. 585-589 ◽  
Author(s):  
David Gottlieb ◽  
Maximiliano Montenegro ◽  
Cristian Millán ◽  
Vicente Díaz ◽  
Karen Hallberg
Keyword(s):  
Nearest Neighbor ◽  
Variational Solution ◽  
Heisenberg Antiferromagnet ◽  
Nearest Neighbor Coupling

scholarly journals NEAR-BOUNDARY AND BULK REGIONS OF A SEMI-INFINITE TWO-DIMENSIONAL HEISENBERG ANTIFERROMAGNET

2010 ◽  
Vol 24 (22) ◽  
pp. 2327-2334 ◽  
Author(s):  
N. VOROPAJEVA ◽  
A. SHERMAN
Keyword(s):  
Spin Wave ◽  
Nearest Neighbor ◽  
Spin Waves ◽  
Two Dimensional ◽  
Heisenberg Antiferromagnet ◽  
Elementary Excitations ◽  
Spin Correlations ◽  
One Dimensional ◽  
Wave Approximation

Using the spin-wave approximation elementary excitations of a semi-infinite two-dimensional S = ½ Heisenberg antiferromagnet are considered. The spectrum consists of bulk modes — standing spin waves and a quasi-one-dimensional mode of boundary spin waves. These latter excitations eject bulk modes from two boundary rows of sites, thereby dividing the antiferromagnet into two regions with different dominant excitations. As a result, absolute values of nearest-neighbor spin correlations on the edge exceed the bulk value.

Range of order in antiferromagnets with next-nearest neighbor coupling

1970 ◽  
Vol 48 (18) ◽  
pp. 2118-2122 ◽  
Author(s):  
John Stephenson
Keyword(s):  
Neutron Diffraction ◽  
Wide Class ◽  
Short Range ◽  
Short Range Order ◽  
Nearest Neighbor ◽  
Range Order ◽  
Two Dimensional ◽  
General Argument ◽  
Nearest Neighbor Coupling

A general argument is presented that a change in the nature of the short-range order will occur above a precisely located temperature TD, the disorder point, for a wide class of magnetic models. The range of order is calculated exactly for two-dimensional asymmetric Ising triangular and union-jack lattices. A sharp cusp in the range of order vs. temperature graph occurs at the disorder point. It is proposed that measurements of the range of order by neutron-diffraction techniques be made on suitable antiferromagnetic crystals to determine whether a disorder point can be detected. It is suggested that two-dimensional antiferromagnets, such as manganese formate dihydrate, may exhibit disorder points.

scholarly journals Semantics of Voids within Data: Ignorance-Aware Machine Learning

2021 ◽  
Vol 10 (4) ◽  
pp. 246
Author(s):  
Vagan Terziyan ◽  
Anton Nikulin
Keyword(s):  
Spatial Data ◽  
Information Science ◽  
Nearest Neighbor ◽  
Geographical Information ◽  
Two Dimensional ◽  
Prototype Selection ◽  
Data Space ◽  
Important Concern ◽  
Traditional Classification ◽  
Nearest Neighbor Classifiers

Operating with ignorance is an important concern of geographical information science when the objective is to discover knowledge from the imperfect spatial data. Data mining (driven by knowledge discovery tools) is about processing available (observed, known, and understood) samples of data aiming to build a model (e.g., a classifier) to handle data samples that are not yet observed, known, or understood. These tools traditionally take semantically labeled samples of the available data (known facts) as an input for learning. We want to challenge the indispensability of this approach, and we suggest considering the things the other way around. What if the task would be as follows: how to build a model based on the semantics of our ignorance, i.e., by processing the shape of “voids” within the available data space? Can we improve traditional classification by also modeling the ignorance? In this paper, we provide some algorithms for the discovery and visualization of the ignorance zones in two-dimensional data spaces and design two ignorance-aware smart prototype selection techniques (incremental and adversarial) to improve the performance of the nearest neighbor classifiers. We present experiments with artificial and real datasets to test the concept of the usefulness of ignorance semantics discovery.

THE CRITICAL BEHAVIOR OF THE 2D SPIN-1 ISING MODEL WITH THE BILINEAR AND POSITIVE BIQUADRATIC NEAREST NEIGHBOR INTERACTIONS ON A CELLULAR AUTOMATON

2004 ◽  
Vol 15 (10) ◽  
pp. 1425-1438 ◽  
Author(s):  
A. SOLAK ◽  
B. KUTLU
Keyword(s):  
Cellular Automaton ◽  
Phase Boundary ◽  
Critical Behavior ◽  
Nearest Neighbor ◽  
Finite Size ◽  
Square Lattice ◽  
Two Dimensional ◽  
Finite Size Scaling ◽  
Creutz Cellular Automaton ◽  
Beg Model

The two-dimensional BEG model with nearest neighbor bilinear and positive biquadratic interaction is simulated on a cellular automaton, which is based on the Creutz cellular automaton for square lattice. Phase diagrams characterizing phase transitions of the model are presented for comparison with those obtained from other calculations. We confirm the existence of the tricritical points over the phase boundary for D/K>0. The values of static critical exponents (α, β, γ and ν) are estimated within the framework of the finite size scaling theory along D/K=-1 and 1 lines. The results are compatible with the universal Ising critical behavior except the points over phase boundary.

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