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Exact Solution of Frenkel-Kontorova Models with a Complete Devil's Staircase in Higher Dimensions

Hsien-chung Kao·Shih-Chang Lee·Wen-Jer Tzeng
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Abstract

We solve exactly a class of Frenkel-Kontorova models with piecewise parabolic potential, which has $d$ sub-wells in a period. With careful analysis, we show that the phase diagram of the minimum enthalpy configurations exhibits the structure of a complete $d$-dimensional devil's staircase. The winding number of a minimum enthalpy configuration is locked to rational values, while the fraction of atoms in each sub-well is locked to values which are sub-commensurable with the winding number.

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Hsien-chung Kao, Shih-Chang Lee, Wen-Jer Tzeng. 1996-07-08. Exact Solution of Frenkel-Kontorova Models with a Complete Devil's Staircase in Higher Dimensions. https://arxiv.org/abs/solv-int/9607001

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