ISING-MODEL ON A CLOSED CAYLEY TREE

An Ising model is considered on a double Cayley tree, where closed graphs of a particularly simple structure are present contrary to the open tree. The existence of such loops strongly supports correlations but is not sufficient for introducing ordinary cooperative behaviour. For this reason the thermodynamic properties are found to differ considerably both from those ones of the open tree and the usual behaviour of the Ising model on regular lattices. There is a phase transition even without external magnetic fields and the correlation function 〈S1S2〉 of certain-not all-pairs of spins of infinite distance exhibits long range order for T < Tc. This phase transition, on the other hand, is not reflected by the specific heat; this quantity is a continuous function of temperature, which is enhanced in comparison with the open tree. © 1979.