Abstract
An Ising model on a regular Cayley tree, with competing ferro- and antiferromagnetic nearest-neighbour interactions, can be formulated as a discrete two-dimensional mapping. The authors use this mapping to obtain sequences of modulated phases, at low temperatures, associated with complete devil's staircases. The fractal dimensionality of the staircases increase with temperature. At high temperatures the incommensurate phases may occupy regions of finite measure of the phase diagram.
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