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

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

1996-07-08

arxiv.org/abs/solv-int/9607001v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

14 pages, uses revtex. Four figures included

Scientific paper

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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