Phase diagrams of the Ising model on the two-fold Cayley tree: phase transition through doubling bifurcation

2004 ◽  
Vol 327 (5-6) ◽  
pp. 374-379 ◽  
Author(s):  
C Ekiz
Keyword(s):  
Phase Transition ◽  
Ising Model ◽  
Phase Diagrams ◽  
Cayley Tree

Behaviors of Phase Diagrams of an Ising Model on a Cayley Tree-Like Lattice: Rectangular Chandelier

2010 ◽  
Author(s):  
Hasan Akin ◽  
Selman Uǧuz ◽  
Seyit Temir ◽  
Theodore E. Simos ◽  
George Psihoyios ◽  
...  
Keyword(s):  
Ising Model ◽  
Phase Diagrams ◽  
Cayley Tree

AN EXACTLY SOLVABLE TWO-FOLD CAYLEY TREE MODEL

1989 ◽  
Vol 03 (10) ◽  
pp. 1523-1537 ◽  
Author(s):  
CAN F. DELALE
Keyword(s):  
Phase Transition ◽  
Ising Model ◽  
Cayley Tree ◽  
Spontaneous Magnetization ◽  
Zero Field ◽  
Tree Graph ◽  
Tree Model ◽  
Exactly Solvable ◽  
Ferromagnetic Ising Model

A two-fold Cayley tree graph with fully q-coordinated sites is constructed and the ferromagnetic Ising model on the constructed graph is solved exactly. It is shown that a phase transition results in zero field at the critical Bethe temperature with spontaneous magnetization below the critical Bethe temperature.

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.

Ground states for the ising model with an external field on the Cayley tree

2018 ◽  
Vol 2018 (3) ◽  
pp. 147-155
Author(s):  
M.M. Rakhmatullaev ◽  
M.A. Rasulova
Keyword(s):  
Ising Model ◽  
External Field ◽  
Cayley Tree ◽  
Ground States
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