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An unorthodox analysis of the Frenkel-Kontorova model

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  • Nasilowski, Ralf

Abstract

The Frenkel-Kontorova model, defined by the Hamiltonian H = Σn=1N (pn22 − K cos xn + (xn − xn−1 − λ)2/2), is a well-known simple 1D model of a many-particle system with two competing types of interaction (interacting particles in a spatially periodic substrate), with a peculiar ground-state behavior which is characterized by “devil's staircase” functions. The statistical mechanics of the FK model reduces to a relatively simple eigenvalue problem, for which we construct a somewhat unorthodox approximate analytic solution, based on an asymptotic formula for the modified Bessel functions. The predictions of our theory are compared with perturbation theoretical predictions and numerically calculated results.

Suggested Citation

  • Nasilowski, Ralf, 1996. "An unorthodox analysis of the Frenkel-Kontorova model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 230(1), pages 266-284.
    • Handle: RePEc:eee:phsmap:v:230:y:1996:i:1:p:266-284
    DOI: 10.1016/0378-4371(95)00411-4
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    1. Kenneth L. Sokoloff & Georgia C. Villaflor, 1979. "Colonial and Revolutionary Muster Rolls: Some New Evidence on Nutrition and Migration in Early America," NBER Working Papers 0374, National Bureau of Economic Research, Inc.
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