Abstract
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.
| Original language | English |
|---|---|
| Pages (from-to) | 2628-2631 |
| Number of pages | 4 |
| Journal | Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics |
| Volume | 55 |
| Issue number | 3 |
| DOIs | |
| Publication status | Published - 1997 |
| Externally published | Yes |
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Statistics and Probability
- Condensed Matter Physics