# Devil's staircase and order without periodicity in classical condensed matter

@article{Aubry1982DevilsSA, title={Devil's staircase and order without periodicity in classical condensed matter}, author={S. Aubry}, journal={Journal De Physique}, year={1982}, volume={44}, pages={147-162} }

The existence of incommensurate structures proves that crystal ordering is not always the most stable one for nonquantum matter. Some properties of structures which are obtained by minimizing a free energy are investigated in the Frenkel Kontorova and related models. It is shown that an incommensurate structure can be either quasi-sinusoidal with a phason mode or built out of a sequence of equidistant defects (discommensurations) which are locked to the lattice by the Peierls force. In that…

## 151 Citations

### Exact models with a complete Devil's staircase

- Physics
- 1983

The author describes two exact models which exhibit a complete Devil's staircase which can both be calculated explicitly with the same method. The first one is a discrete Frenkel-Kontorova model (an…

### The Transition by Breaking of Analyticity in Incommensurate Structures and the Devil’s Staircase; Application to Metal-Insulator Transitions in Peierls Chains

- Physics
- 1983

We review results which have been obtained on the “transition by breaking of analyticity” in incommensurate structures, that is in other words the transition by the lattice locking of an…

### Locking to incommensurate structures

- Physics
- 1986

Abstract A classical pseudo-spin model in one dimension is considered, representing a variation on the Frenkel—Kontorova model to include non-convex interactions, resulting in three competing length…

### Locking to incommensurate structures-a model with three competing lengths

- Physics
- 1985

A classical pseudo-spin model in one dimension is considered, representing a variation on the Frenkel-Kontorova model to include non-convex interactions, resulting in three competing length scales.…

### Long period structures in Ti1+xAl3−x alloys: experimental evidence of a devil's staircase?

- Materials Science
- 1985

Long period antiphase boundary structures based on the L1 2 type structure have been studied in Ti 1+x Al 3−x alloys by electron diffraction and high resolution electron microscopy. The domain of…

### Low-temperature excitations, specific heat and hierarchical melting of a one-dimensional incommensurate structure

- Physics
- 1988

The low-temperature behaviour of an Ising spin model for a one-dimensional incommensurate structure (which is equivalent to the discrete Frenkel-Kontorova model in the non-analytical regime) is…

### Subatomic movements of a domain wall in the Peierls potential

- PhysicsNature
- 2003

It is revealed that domain walls can become trapped between crystalline planes, and that they propagate by distinct jumps that match the lattice periodicity, which offers a means for probing experimentally the physics of topological defects in discrete lattices.

### Incommensurate structure with no average lattice : an example of a one-dimensional quasicrystal

- Physics
- 1987

We study the ground state of a simple one-dimensional model describing an incommensurate modulation of the vacancy density of a periodic lattice. We show that this structure, through its Fourier…

### Symmetry-breaking commensurate states in generalised Frenkel-Kontorova models

- Physics
- 1989

Ground states of classical, one-dimensional systems consisting of atoms connected with harmonic springs subject to a periodic, symmetric potential are studied. It is shown that some choices of the…

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