Strange Attractor in the Ising Model with Competing Interactions on the Cayley Tree

We formulate the Ising model with competing interactions on a Cayley tree, in the infinite-coordination limit, as a two-dimensional nonlinear mapping. The phase diagram displays a Lifshitz point and many modulated phases. We perform calculations to show the existence of a complete devil's staircase at low temperatures. Also, we give strong numerical evidence for the existence of chaotic phases associated with strange attractors.

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