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

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-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 $D_0$ associated with these fractal structures, and show that $D_0$ increases with temperature but seems to reach a limiting value smaller than $D_0=1$.

17 pages, 6 figures

References in corpus (2)

• Monte Carlo Study of the Axial Next-Nearest-Neighbor Ising Model
• A Monte Carlo Approach for Studying Microphases Applied to the Axial Next-Nearest-Neighbor Ising and the Ising-Coulomb Models

Cited by in corpus (4)

• Modulated phases in a three-dimensional Maier-Saupe model with competing interactions
• Modulated structures in a Lebwohl-Lasher model with chiral interactions
• Modulated phases in a spin model with Dzyaloshinskii-Moriya interactions
• Supersolid Devil's Staircases of Spin-Orbit-Coupled Bosons in Optical Lattices