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

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.

scholarly journals Onp-adic Gibbs measures of the countable state Potts model on the Cayley tree

Nonlinearity ◽  
2007 ◽  
Vol 20 (12) ◽  
pp. 2923-2937 ◽  
Author(s):  
A Yu Khrennikov ◽  
F M Mukhamedov ◽  
J F F Mendes
Keyword(s):  
Potts Model ◽  
Cayley Tree ◽  
Gibbs Measures ◽  
Countable State

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

THE SHANNON–MCMILLAN THEOREM FOR MARKOV CHAINS INDEXED BY A CAYLEY TREE IN RANDOM ENVIRONMENT

2017 ◽  
Vol 32 (4) ◽  
pp. 626-639 ◽  
Author(s):  
Zhiyan Shi ◽  
Pingping Zhong ◽  
Yan Fan
Keyword(s):  
Markov Chains ◽  
State Space ◽  
Random Environment ◽  
Cayley Tree ◽  
Law Of Large Numbers ◽  
Strong Law ◽  
Countable State Space ◽  
Large Numbers ◽  
Countable State ◽  
Definition Of

In this paper, we give the definition of tree-indexed Markov chains in random environment with countable state space, and then study the realization of Markov chain indexed by a tree in random environment. Finally, we prove the strong law of large numbers and Shannon–McMillan theorem for Markov chains indexed by a Cayley tree in a Markovian environment with countable state space.

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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