Constructive Gibbs Measures for the Three-State Ising–Potts Model on a Cayley Tree

We consider a mixed-type model, namely the Ising–Potts model on a Cayley tree. For this model, under certain assumptions on the parameter, we show that there exist at least three translation-invariant Gibbs measures on a Cayley tree of order $$k\ge 2$$ . We also study constructive Gibbs measures for the Ising–Potts model on a Cayley tree, and show the existence of new constructive Gibbs measures for this model on a Cayley tree.

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