Periodic Gibbs Measures and Their Extremality for the HC-Blume–Capel Model in the Case of a Wand with a Chemical Potential on a Cayley Tree

Periodic Gibbs measures for the HC-Blume–Capel model with a chemical potential with parameters $$(\theta,\eta)$$ on a Cayley tree in the case of a wand graph are studied. We prove that in this case for $$\theta^3\le\eta$$ there exist precisely three periodic Gibbs measures, all of which are translation-invariant, while for $$\theta^3>\eta$$ there exist precisely three periodic Gibbs measures, one of which is translation-invari The (non)extremality of these measures is also studied.

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