The Exact Ground State of the Frenkel-Kontorova Model with Repeated Parabolic Potential: I. Basic Results

Details The Exact Ground State of the Frenkel-Kontorova Model with Repeated Parabolic Potential: I. Basic Results The Exact Ground State of the Frenkel-Kontorova Model with Repeated Parabolic Potential: I. Basic Results

1997-07-22

arxiv.org/abs/cond-mat/9707227v1

Phys. Rev. B56, 8623-8630 (1997)

Physics

Condensed Matter

Statistical Mechanics

12 RevTeX pages, using AMS-Fonts (amssym.tex,amssym.def), 6 Postscript figures, accepted by Phys. Rev. B

Scientific paper

10.1103/PhysRevB.56.8623

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.

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