Journal of Statistical Physics

, Volume 80, Issue 1–2, pp 45–67 | Cite as

The classical statistical mechanics of Frenkel-Kontorova models

  • R. S. MacKay


The scaling properties of the free energy, specific heat, and mean spacing are calculated for classical Frenkel-Kontorova models at low temperature, in three regimes: near the integrable limit, the anti-integrable limit, and the sliding-pinned transition (“transition by breaking of analyticity”). In particular, the renormalization scheme given in previous work for ground states of Frenkel-Kontorova models is extended to nonzero-temperature Gibbs states, and the hierarchical melting phenomenon of Vallet, Schilling, and Aubry is put on a rigorous footing.

Key Words

Renormalization scaling specific heat anti-integrable limit sliding-pinned transition 


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Copyright information

© Plenum Publishing Corporation 1995

Authors and Affiliations

  • R. S. MacKay
    • 1
    • 2
  1. 1.Nonlinear Systems Laboratory, Mathematics InstituteUniversity of WarwickCoventryUK
  2. 2.Centre de Dynamique des Systèmes Complexes/Laboratoire de Topologie URA CNRS 755, Département de MathématiquesUniversité de BourgogneDijonFrance

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