scholarly journals On the uniqueness of Gibbs measure in the Potts model on a Cayley tree with external field

2019 ◽  
Vol 2019 (7) ◽  
pp. 073205
Author(s):  
Leonid V Bogachev ◽  
Utkir A Rozikov
Keyword(s):  
External Field ◽  
Gibbs Measure ◽  
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.

On uniqueness of Gibbs measure for -adic countable state Potts model on the Cayley tree

2009 ◽  
Vol 71 (11) ◽  
pp. 5327-5331 ◽  
Author(s):  
Andrei Khrennikov ◽  
Farrukh Mukhamedov
Keyword(s):  
Gibbs Measure ◽  
Potts Model ◽  
Cayley Tree ◽  
Countable State

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

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
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