Weakly periodic ground states and Gibbs measures for the Ising model with competing interactions on the Cayley tree.

We introduce the notion of a weakly periodic configuration. For the Ising model with competing interactions, we describe the set of all weakly periodic ground states corresponding to normal divisors of indices 2 and 4 of the group representation of the Cayley tree. In addition, we study new Gibbs measures for the Ising model. [ABSTRACT FROM AUTHOR]