Correlation Functions of the Ising Model with Multisite Interaction on   the Husimi Lattice
  We consider a general spin-1/2 Ising model with multisite interaction on the Husimi lattice with the coordination number q and derive an analytical expression of correlation functions for stable fixed points of the corresponding recurrence relation. We show that for q=2 our model transforms to the two-state vertex model on the Bethe lattice with q=3 and for the case q=3, with only nearest neighbour interactions, we transform our model to the corresponding model on the Bethe lattice with q=3, using the Yang-Baxter equations. 
N.S. Ananikian, R.G. Ghulghazaryan, N.Sh. Izmailian