Farey fractions and the Frenkel-Kontorova model

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Title:	Farey fractions and the Frenkel-Kontorova model
Authors:	Kao, Hsien-chung;Lee, Shih-Chang;Tzeng, Wen-Jer
Contributors:	淡江大學物理學系
Keywords:	Exactly Solvable and Integrable Systems (nlin.SI);Condensed Matter (cond-mat)
Date:	1997-03
Issue Date:	2013-07-09 15:18:03 (UTC+8)
Publisher:	College Park: American Physical Society
Abstract:	We solved the Frenkel-Kontorova model with the potential V(u)=-λ(u-Int[u]-1/2)2/2 exactly. For given λ>0, there exists a positive integer qc such that the winding number ω of the minimum enthalpy state is locked to rational numbers in the qcth row of Farey fractions. For fixed ω=p/q, there is a critical λc when a first order phase transition occurs. This phase transition can be understood as the dissociation of a large molecule into two smaller ones in a manner dictated by the Farey fractions.
Relation:	Physical Review E (Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics) 55(3), pp.2628-2631
DOI:	10.1103/PhysRevE.55.2628
Appears in Collections:	[Graduate Institute & Department of Physics] Journal Article

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