Description of weakly periodic Gibbs measures for the isingmodel on a cayley tree.

We introduce the concept of a weakly periodic Gibbs measure. For the Ising model, we describe a set of such measures corresponding to normal subgroups of indices two and four in the group representation of a Cayley tree. In particular, we prove that for a Cayley tree of order four, there exist critical values T c < T cr of the temperature T > 0 such that there exist five weakly periodic Gibbs measures for 0 < T < T c or T > T cr , three weakly periodic Gibbs measures for T = T c , and one weakly periodic Gibbs measure for T c < T ≤ T cr . [ABSTRACT FROM AUTHOR]