  A discrete Frenkel-Kontorova model with two alternate spring constants
$k_{1}$ and $k_{2}$ is studied. It is found that this model has many surprising
behaviours. The continuum version of this model is different from the
sine-Gordon equation, which is the continuum version of the standard FK model.
More interestingly, it has an unpinned commensurate phase which is
translationally invariant. A phase transition takes place on a lattice point in
the parameter space. We have also predicted another interesting phase
transition in which an unlocked commensurate phase breaking translational
invariance will take place as the strength of the substrate potential is
increased.
