Energy extremes and spin configurations for the one‐dimensional antiferromagnetic Ising model with arbitrary‐range interaction

1996 ◽  
Vol 37 (7) ◽  
pp. 3334-3353 ◽  
Author(s):  
Jack Douthett ◽  
Richard Krantz
Keyword(s):  
Ising Model ◽  
Range Interaction ◽  
One Dimensional ◽  
Antiferromagnetic Ising Model ◽  
The One

scholarly journals ONE-DIMENSIONAL LONG-RANGE FERROMAGNETIC ISING MODEL UNDER WEAK AND SPARSE EXTERNAL FIELD

2009 ◽  
Vol 23 (32) ◽  
pp. 5899-5906
Author(s):  
AZER KERIMOV
Keyword(s):  
Ising Model ◽  
External Field ◽  
Long Range ◽  
Low Temperatures ◽  
Gibbs State ◽  
Range Interaction ◽  
One Dimensional ◽  
Long Range Interaction ◽  
Ferromagnetic Ising Model ◽  
The One

We consider the one-dimensional ferromagnetic Ising model with very long range interaction under weak and sparse biased external field and prove that at sufficiently low temperatures, the model has a unique limiting Gibbs state.

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