TY - JOUR
T1 - Farey fractions and the Frenkel-Kontorova model
AU - Kao, Hsien chung
AU - Lee, Shih Chang
AU - Tzeng, Wen Jer
PY - 1997
Y1 - 1997
N2 - We solved the Frenkel-Kontorova model with the potential V(u)=-λ(u-Int[u]-1/2[formula presented]/2 exactly. For given λ>0, there exists a positive integer [formula presented] such that the winding number ω of the minimum enthalpy state is locked to rational numbers in the [formula presented]th row of Farey fractions. For fixed ω=p/q, there is a critical [formula presented] 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.
AB - We solved the Frenkel-Kontorova model with the potential V(u)=-λ(u-Int[u]-1/2[formula presented]/2 exactly. For given λ>0, there exists a positive integer [formula presented] such that the winding number ω of the minimum enthalpy state is locked to rational numbers in the [formula presented]th row of Farey fractions. For fixed ω=p/q, there is a critical [formula presented] 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.
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U2 - 10.1103/PhysRevE.55.2628
DO - 10.1103/PhysRevE.55.2628
M3 - Article
AN - SCOPUS:0642316182
SN - 1063-651X
VL - 55
SP - 2628
EP - 2631
JO - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
JF - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
IS - 3
ER -