Numerical study of a new type of nonconvex Frenkel-Kontorova model

Bassler, Kevin E.; Griffiths, Robert B.

doi:10.1103/physrevb.49.904

Cited by 10 publications

(2 citation statements)

References 25 publications

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“…First, it provides a simple example which exhibits some of the complex phenomena (discommensurations, devil's staircase phase diagrams) associated with commensurate-incommensurate phase transitions [5]. For some recent studies, see [6,7]; also [8] for extensions to quantum systems, and [9] for classical particles at a finite temperature. Next, various interesting dynamical phenomena result if forces, either static or dynamic, are applied to the particles in a Frenkel-Kontorova chain; for some recent work, see [10,11].…”

Section: Introductionmentioning

confidence: 99%

Exact ground state of the Frenkel-Kontorova model with repeated parabolic potential. I. Basic results

1997

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The problem of finding the exact energies and configurations for the Frenkel-Kontorova model consisting of particles in one dimension connected to their nearest-neighbors by springs and placed in a periodic potential consisting of segments from parabolas of identical (positive) curvature but arbitrary height and spacing, is reduced to that of minimizing a certain convex function defined on a finite simplex.64.70. Rh, 64.60.Ak, 61.44.+p, 05.45.+b

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Section: Introductionmentioning

confidence: 99%

Exact ground state of the Frenkel-Kontorova model with repeated parabolic potential. I. Basic results

1997

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“…For example, it is possible to encounter a situation with a dimer particle sub-staircase in the particle sector and a trimer hole sub-staircase in the hole sector. Finally, we would like to note that the impact of different kinds of interactions on the devil's staircase physics has been studied in the literature from different perspectives [36][37][38][39][40][41][42][43] . For example, some aspects of the staircases discussed in the present work can be linked to studies of atoms adsorbed on a surface 38,40 .…”

Section: Introductionmentioning

confidence: 99%

Devil's staircases without particle-hole symmetry

Lan

Lesanovsky

2018

Phys. Rev. B

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We present and analyze spin models with long-range interactions whose ground state features a so-called devil's staircase and where plateaus of the staircase are accessed by varying two-body interactions. This is in contrast to the canonical devil's staircase, for example, occurring in the one-dimensional Ising model with long-range interactions, where typically a single-body chemical potential is varied to scan through the plateaus. These systems, moreover, typically feature a particle-hole symmetry which trivially connects the hole part of the staircase (filling fraction f 1/2) to its particle part (f 1/2). Such symmetry is absent in our models and hence the particle sector and the hole sector can be separately controlled, resulting in exotic hybrid staircases.

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Ground state of one-dimensional chiral XY model under external magnetic field and uniaxial potential

Monma

Horiguchi

1997

Physica A: Statistical Mechanics and its Applications

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Numerical study of a new type of nonconvex Frenkel-Kontorova model

Cited by 10 publications

References 25 publications

Exact ground state of the Frenkel-Kontorova model with repeated parabolic potential. I. Basic results

Exact ground state of the Frenkel-Kontorova model with repeated parabolic potential. I. Basic results

Devil's staircases without particle-hole symmetry

Ground state of one-dimensional chiral XY model under external magnetic field and uniaxial potential

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