Field behavior of an Ising model with competing interactions on the Bethe lattice

We consider an Ising model with competing interactions on a Bethe lattice in the presence of a magnetic field. In the infinite-coordination limit, the problem reduces to the study of a two-dimensional mapping. We study in detail the properties of this mapping with particular emphasis on the location of the stable periodic orbits, corresponding to commensurate structures of the model, on the field-temperature plane for different strengths of the competing interactions. We develop some efficient numerical procedures for this purpose. We also investigate the existence of strange attractors on the model in the presence of a field.

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