Abstract
We study the low—temperature properties of quasi one—dimensional, incommensurate structures which are described by a Frenkel—Kontorova—like model. A new type of renormalization method will be presented, which is determined by the continued fraction expansion of the incommensurability ratio ζ. (This method yields a hierarchy of renormalized Hamiltonians ϰ(n,p) describing the thermal behavior for temperatures T = O(T(n,p)), where T(n,p) follows from the continued fraction expansion of ζ. By means of this method the low—temperature specific heat c(T) and the static structure factor S(q) are calculated for fixed ζ. c(T) possesses a hierarchy of Schottky anomalies related to the rational approximates of ζ and S(q) exhibits more and more satellites when the temperature is decreased. Our theoretical approach predicts a high sensitivity on a small change of ζ. For instance c(T) and S(q) may change by several orders of magnitude if ζ is changed by, e.g one per cent only. Finally our results are compared with experimental data.
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Schilling, R. (1993). Hierarchical Melting of One-Dimensional Incommensurate Structures. In: Riste, T., Sherrington, D. (eds) Phase Transitions and Relaxation in Systems with Competing Energy Scales. NATO ASI Series, vol 415. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-1908-5_13
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DOI: https://doi.org/10.1007/978-94-011-1908-5_13
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