Periodic and weakly periodic Gibbs measures for the Kittel’s molecular zipper model on the Cayley tree

In the present work, we study periodic and weakly periodic Gibbs measures for the model on the Cayley tree of order $k\geq 1$ and we show that all periodic Gibbs measures coincide with translation-invariant Gibbs measures and prove the existence of non-translation-invariant weakly periodic Gibbs measures.