Effective Potentials: A New Approach and New Results for One-Dimensional Systems with Competing Length Scales
- 5 May 1986
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review Letters
- Vol. 56 (18) , 1929-1931
- https://doi.org/10.1103/physrevlett.56.1929
Abstract
A new method, involving the solution of a nonlinear eigenvalue equation, is proposed for finding the ground-state configurations and energies of the Frenkel-Kontorova and similar onedimensional models which can show complicated transitions between commensurate and incommensurate phases. It is used to show that a distinctive phase diagram can arise if a cosine potential is perturbed by the addition of suitable harmonics.Keywords
This publication has 15 references indexed in Scilit:
- Percival variational principle for invariant measures and commensurate-incommensurate phase transitions in one-dimensional chainsCommunications in Mathematical Physics, 1984
- Devil's staircase in a one-dimensional modelPhysical Review B, 1984
- Aubry transition in a finite modulated chainPhysical Review B, 1984
- Pinning transition of the discrete sine-Gordon equationPhysical Review B, 1983
- Critical behaviour at the transition by breaking of analyticity in the discrete Frenkel-Kontorova modelJournal of Physics C: Solid State Physics, 1983
- Devil's staircase and order without periodicity in classical condensed matterJournal de Physique, 1983
- Commensurate-incommensurate phase transitions in one-dimensional chainsJournal of Statistical Physics, 1982
- Commensurate phases, incommensurate phases and the devil's staircaseReports on Progress in Physics, 1982
- Critical behavior of a KAM surface: I. Empirical resultsJournal of Statistical Physics, 1982
- A method for determining a stochastic transitionJournal of Mathematical Physics, 1979