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.
|頁（從 - 到）||2628-2631|
|期刊||Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics|
|出版狀態||已發佈 - 1997|
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