60 40 01 v 1 1 6 A pr 1 99 6 Farey Tree and the Frenkel - Kontorova Model
نویسنده
چکیده
We solved the Frenkel-Kontorova model with the potential V (u) = − 2 |λ|(u− Int[u]− 1 2) 2 exactly. For given |λ|, there exists a positive integer qc such that for almost all values of the tensile force σ, the winding number ω of the ground state configuration is a rational number in the qc-th level Farey tree. 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 tree. A kind of “commensurate-incommensurate” transition occurs at critical values of σ when two sizes of molecules co-exist. “Soliton” in the usual sense does not exist but induces a transformation of one size of molecules into the other. PACS number(s):03.20.+i, 05.45.+b, 64.60.-i Typeset using REVTEX 1
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تاریخ انتشار 1996