  We consider a Frenkel-Kontorova system of harmonic oscillators in a
two-dimensional Euclidean lattice and we obtain a quantitative estimate on the
angular function of the equilibria. The proof relies on a PDE method related to
a classical conjecture by E. De Giorgi, also in view of an elegant technique
based on complex variables that was introduced by A. Farina.
  In the discrete setting, a careful analysis of the reminders is needed to
exploit this type of methodologies inspired by continuum models.
