dorsal/arxiv
View SchemaExact Solution of Frenkel-Kontorova Models with a Complete Devil's Staircase in Higher Dimensions
| Authors | Hsien-chung Kao, Shih-Chang Lee, Wen-Jer Tzeng |
|---|---|
| Categories | |
| ArXiv ID | solv-int/9607001 |
| URL | https://arxiv.org/abs/solv-int/9607001 |
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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"abstract": "We solve exactly a class of Frenkel-Kontorova models with piecewise parabolic\npotential, which has $d$ sub-wells in a period. With careful analysis, we show\nthat the phase diagram of the minimum enthalpy configurations exhibits the\nstructure of a complete $d$-dimensional devil\u0027s staircase. The winding number\nof a minimum enthalpy configuration is locked to rational values, while the\nfraction of atoms in each sub-well is locked to values which are\nsub-commensurable with the winding number.",
"arxiv_id": "solv-int/9607001",
"authors": [
"Hsien-chung Kao",
"Shih-Chang Lee",
"Wen-Jer Tzeng"
],
"categories": [
"solv-int",
"nlin.SI"
],
"title": "Exact Solution of Frenkel-Kontorova Models with a Complete Devil\u0027s Staircase in Higher Dimensions",
"url": "https://arxiv.org/abs/solv-int/9607001"
},
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"execution_id": "223f8363-05fc-49f9-99f7-2d7ff71d0f9f",
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"type": "Model",
"variant": "snapshot-2026-03-01",
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