Abstract
Lattice spin systems with multisite interactions have rich and interesting phase diagrams. We present some results for such systems involving Ising spins (σ=±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.
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Monroe, J.L. Phase diagrams of Ising models on Husimi trees. I. Pure multisite interaction systems. J Stat Phys 65, 255–268 (1991). https://doi.org/10.1007/BF01329860
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DOI: https://doi.org/10.1007/BF01329860