Extremality of translation-invariant Gibbs measures for the $$\lambda$$ -model on the binary Cayley tree

Theoretical and Mathematical Physics - We consider the $$\lambda$$ -model on the Cayley tree of order $$k=2$$ . Under some conditions, we study translation-invariant Gibbs measures. Moreover, we...     

On the Constructive Description of Gibbs Measures for the Potts Model on a Cayley Tree

Ukrainian Mathematical Journal - We consider the Potts model on a Cayley tree and prove the existence of Gibbs measures constructed by the method proposed in [H. Akin, U. A. Rozikov, and S. Temir,...     

A p-Adic Generalized Gibbs Measure for the Ising Model on a Cayley Tree

Theoretical and Mathematical Physics - We consider a p-adic Ising model on the Cayley tree of order k ≥ 2. We completely describe all p-adic-translation-invariant generalized Gibbs measures...     

Periodic Ground States for the Potts Model with External Field and a Countable Set of Spin Values on the Cayley Tree

Mathematical Notes - For the Potts model with external field and a countable set of spin values on the Cayley tree of order $$k\ge2$$ , the set of periodic ground states corresponding to normal...     

The existence of weakly periodic Gibbs measures for the Potts model on a Cayley tree

We study the q-state Potts model on a Cayley tree of order k ≥ 2. In the group representation of the Cayley tree for the ferromagnetic Potts model, we single out a set of index-2 subgroups under which each weakly periodic Gibbs measure is translation invariant. For the anti-ferromagnetic Potts model with k ≥ 2 and q ≥ 2, we show that a weakly periodic Gibbs measure that is not translation invariant is not unique.