scholarly journals Connection-matrix eigenvalues in the Ising model: taking into account interaction with next-nearest neighbors

2019 ◽  
Vol 489 (3) ◽  
pp. 246-249
Author(s):  
B. V. Kryzhanovsky ◽  
L. B. Litinskii
Keyword(s):  
Ising Model ◽  
Nearest Neighbors ◽  
Connection Matrix ◽  
Eigenvalues And Eigenvectors ◽  
One Dimensional ◽  
Free Boundary Conditions ◽  
Matrix Eigenvalues ◽  
The One ◽  
Exact Relations ◽  
Account Interaction

The connection matrix of the Ising model on a d-dimensional hypercube is investigated. In addition to the interactions between the nearest neighbors, the interactions between the next-nearest neighbors are taken into account. For such a matrix, the exact relations for the eigenvalues and eigenvectors, which are reasonably simply expressed through the corresponding characteristics of the one-dimensional Ising model, are obtained. Both periodic and free boundary conditions are considered.

ON THE TEMPERATURE DEPENDENCE OF PARAMAGNETIC RESONANCE IN THE CASE OF THE ISING MODEL

1961 ◽  
Vol 39 (12) ◽  
pp. 1733-1737 ◽  
Author(s):  
Y. Y. Lee
Keyword(s):  
Ising Model ◽  
Temperature Dependence ◽  
Approximation Method ◽  
Line Shape ◽  
Theoretical Study ◽  
Shape Function ◽  
Paramagnetic Resonance ◽  
One Dimensional ◽  
The One ◽  
Line Shape Function

The adequacy of the approximation method used by McMillan and Opechowski in their theoretical study of the temperature dependence of the paramagnetic resonance line shape function is very difficult to ascertain for the case of a typical paramagnetic crystal. For this reason the approximation method has been investigated for the very simple case of the one-dimensional Ising model. Exact expressions for the line shape function of the model are compared with expressions obtained by the approximation method mentioned above. The agreement between the two expressions is found to be very good in general, and extremely good at very low temperatures.

On the one-dimensional ising model with arbitrary spin

1976 ◽  
Vol 37 (7-8) ◽  
pp. 803-811 ◽  
Author(s):  
R.L. Bowden ◽  
D.M. Kaplan
Keyword(s):  
Ising Model ◽  
Arbitrary Spin ◽  
One Dimensional ◽  
The One
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