Mean field phase diagram of the discrete Frenkel-Kontorova model

The mean field phase diagram of the discrete Frenkel-Kontorova model (harmonic chain of particles exposed to a sinusoidal potential) is studied using a fixed irrational value for the ratio of atoms and available sites as a boundary condition. Independent variables are the temperature and the height of the sinusoidal potential. The phase diagram contains two different solid phases, namely an intrinsically pinned incommensurate and an unpinned incommensurate phase. The position of the phase boundary and the nature of the phases are determined. We also investigate the influence of an electric field and the resulting pinning-unpinning transition for fields smaller than the threshold field.