A New Set of Limiting Gibbs Measures for the Ising Model on a Cayley Tree

For the Ising model (with interaction constant J > 0) on the Cayley tree of order k >= 2 it is known that for the temperature T >= T-c,T-k = J/arctan (1/k) the limiting Gibbs measure is unique, and for T < T-c,T-k there are uncountably many extreme Gibbs measures. In the Letter we show that if T is an element of (T-c,T-root k, T-c,T-k0), with root k < k(0) < k then there is a new un-countable set G(k,k0) of Gibbs measures. Moreover G(k,k0) not equal G(k,k'0), for k(0) not equal k'(0). Therefore if T is an element of (T-c,(root k), T-c,T-root k+ 1), T-c,(root k+ 1) < T-c,T-k then the set of limiting Gibbs measures of the Ising model contains the set {known Gibbs measures}boolean OR(U-k0:root k