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Modulated phases and devil’s staircases in a layered mean-field version of the ANNNI model

Author

Listed:
  • Nascimento, E.S.
  • de Lima, J.P.
  • Salinas, S.R.

Abstract

We investigate the phase diagram of a spin-1/2 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-field 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 D0 associated with these fractal structures, and show that D0 increases with temperature but seems to reach a limiting value smaller than D0=1.

Suggested Citation

  • Nascimento, E.S. & de Lima, J.P. & Salinas, S.R., 2014. "Modulated phases and devil’s staircases in a layered mean-field version of the ANNNI model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 409(C), pages 78-86.
    • Handle: RePEc:eee:phsmap:v:409:y:2014:i:c:p:78-86
    DOI: 10.1016/j.physa.2014.04.045
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