EXACT GROUND-STATE OF THE FRENKEL-KONTOROVA MODEL WITH REPEATED PARABOLIC POTENTIAL .2. NUMERICAL TREATMENT

A procedure is described for efficiently finding the ground-state ener gy and configuration for a Frenkel-Kontorova model in a periodic poten tial, consisting of N parabolic segments of identical curvature in eac h period, through a numerical solution of the convex minimization prob lem described in the preceding paper. The key elements are the use of subdifferentials to describe the structure of the minimization problem ; an intuitive picture of how to solve it, based on motion of quasipar ticles; and a fast linear optimization method with a reduced memory re quirement. The procedure has been tested for N up to 200.