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Modulated phases and devil's staircases in a layered mean-field version of the ANNNI model
We investigate the phase diagram of a spin- Ising model on a cubic
lattice, with competing interactions between nearest and next-nearest neighbors
along an axial direction, and fully connected spins on the sites of each
perpendicular layer. The problem is formulated in terms of a set of
noninteracting Ising chains in a position-dependent field. At low temperatures,
as in the standard mean-feild version of the Axial-Next-Nearest-Neighbor Ising
(ANNNI) model, there are many distinct spatially commensurate phases that
spring from a multiphase point of infinitely degenerate ground states. As
temperature increases, we confirm the existence of a branching mechanism
associated with the onset of higher-order commensurate phases. We check that
the ferromagnetic phase undergoes a first-order transition to the modulated
phases. Depending on a parameter of competition, the wave number of the striped
patterns locks in rational values, giving rise to a devil's staircase. We
numerically calculate the Hausdorff dimension associated with these
fractal structures, and show that increases with temperature but seems
to reach a limiting value smaller than .Comment: 17 pages, 6 figure
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