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 Tc < Tcr of the temperature T > 0 such that there exist five weakly periodic Gibbs measures for 0 < T < Tc or T > Tcr, three weakly periodic Gibbs measures for T = Tc, and one weakly periodic Gibbs measure for Tc < T ≤ Tcr.