Ising model on the Cayley tree with competing interactions up to the third Nearest-neighbors with spins belonging to different branches of the tree

2015 ◽  
Vol 66 (8) ◽  
pp. 1200-1206 ◽  
Author(s):  
Nasir Ganikhodjaev ◽  
Mohd Hirzie Mohd Rodzhan
Keyword(s):  
Ising Model ◽  
Cayley Tree ◽  
Nearest Neighbors ◽  
Competing Interactions ◽  
The Third

Ising model with competing interactions on a Cayley tree

1983 ◽  
Vol 33 (2) ◽  
pp. 419-436 ◽  
Author(s):  
Sakari Inawashiro ◽  
Colin J. Thompson ◽  
Goshi Honda
Keyword(s):  
Ising Model ◽  
Cayley Tree ◽  
Competing Interactions

scholarly journals Exact solution of an Ising model with competing interactions on a Cayley tree

2003 ◽  
Vol 36 (15) ◽  
pp. 4283-4289 ◽  
Author(s):  
N N Ganikhodjaev ◽  
C H Pah ◽  
M R B Wahiddin
Keyword(s):  
Exact Solution ◽  
Ising Model ◽  
Cayley Tree ◽  
Competing Interactions

Phase diagram of the Ising Model on a Cayley tree in the presence of competing interactions and magnetic field

1985 ◽  
Vol 40 (3-4) ◽  
pp. 577-592 ◽  
Author(s):  
Ananias M. Mariz ◽  
Constantino Tsallis ◽  
E. L. Albuquerque
Keyword(s):  
Magnetic Field ◽  
Phase Diagram ◽  
Ising Model ◽  
Cayley Tree ◽  
Competing Interactions

scholarly journals Phase transition and Gibbs measures of Vannimenus model on semi-infinite Cayley tree of order three

2017 ◽  
Vol 31 (13) ◽  
pp. 1750093 ◽  
Author(s):  
Hasan Akın
Keyword(s):  
Phase Transition ◽  
Ising Model ◽  
Cayley Tree ◽  
Gibbs Measures ◽  
Bethe Lattice ◽  
Nearest Neighbors ◽  
Translation Invariant ◽  
New Approach ◽  
Gibbs Distributions

Ising model with competing nearest–neighbors (NN) and prolonged next–nearest–neighbors (NNN) interactions on a Cayley tree has long been studied, but there are still many problems untouched. This paper tackles new Gibbs measures of Ising–Vannimenus model with competing NN and prolonged NNN interactions on a Cayley tree (or Bethe lattice) of order three. By using a new approach, we describe the translation-invariant Gibbs measures (TIGMs) for the model. We show that some of the measures are extreme Gibbs distributions. In this paper, we try to determine when phase transition does occur.

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