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RESEARCH PRODUCT
The classical statistical mechanics of Frenkel-Kontorova models
Robert S. MackayRobert S. Mackaysubject
PhysicsRenormalizationWork (thermodynamics)Integrable systemSpecific heatQuantum mechanicsScheme (mathematics)Statistical and Nonlinear PhysicsStatistical physicsStatistical mechanicsLimit (mathematics)ScalingMathematical Physicsdescription
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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 1995-07-01 | Journal of Statistical Physics |