Phase diagrams of Ising models on Husimi trees. I. Pure multisite interaction systems

Lattice spin systems with multisite interactions have rich and interesting phase diagrams. We present some results for such systems involving Ising spins (=±1) using a generalization of the Bethe lattice approximation. First, we show that our approach yields good approximations for the phase diagrams of some recently studied multisite interaction systems. Second, a multisite interaction system with competing interactions is investigated and a strong connection with results from the theory of dynamical systems is made. We exhibit a full bifurcation diagram, chaos, period-3 windows, etc., for the magnetization of the base site of this system.