The disordered phase of the inhomogeneous potts model is extremal on the Cayley tree

2000 ◽  
Vol 124 (3) ◽  
pp. 1202-1210 ◽  
Author(s):  
F. M. Mukhamedov ◽  
U. A. Rozikov
Keyword(s):  
Potts Model ◽  
Cayley Tree ◽  
Disordered Phase

Modulated Phase of a Potts Model with Competing Binary Interactions on a Cayley Tree

2009 ◽  
Vol 137 (4) ◽  
pp. 701-715 ◽  
Author(s):  
N. Ganikhodjaev ◽  
S. Temir ◽  
H. Akin
Keyword(s):  
Potts Model ◽  
Cayley Tree ◽  
Modulated Phase

Metastability in the Potts model on the Cayley tree

1991 ◽  
Vol 64 (3-4) ◽  
pp. 673-682 ◽  
Author(s):  
F. S. de Aguiar ◽  
L. B. Bernardes ◽  
S. Goulart Rosa
Keyword(s):  
Potts Model ◽  
Cayley Tree

scholarly journals ON INHOMOGENEOUS p-ADIC POTTS MODEL ON A CAYLEY TREE

2005 ◽  
Vol 08 (02) ◽  
pp. 277-290 ◽  
Author(s):  
FARRUKH MUKHAMEDOV ◽  
UTKIR ROZIKOV
Keyword(s):  
Gibbs Measure ◽  
Potts Model ◽  
Cayley Tree ◽  
Nearest Neighbor ◽  
Gibbs Measures ◽  
Nearest Neighbors ◽  
Translation Invariant

We consider a nearest-neighbor inhomogeneous p-adic Potts (with q≥2 spin values) model on the Cayley tree of order k≥1. The inhomogeneity means that the interaction Jxy couplings depend on nearest-neighbors points x, y of the Cayley tree. We study (p-adic) Gibbs measures of the model. We show that (i) if q∉pℕ then there is unique Gibbs measure for any k≥1 and ∀ Jxy with | Jxy |< p-1/(p -1). (ii) For q∈p ℕ, p≥3 one can choose Jxy and k≥1 such that there exist at least two Gibbs measures which are translation-invariant.

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