Frenkel-Kontorova Model: Commensurate-Incommensurate Transition
A chain of atoms in a periodic substrate potential — explore the devil's staircase and soliton (kink) formation as the natural spacing changes.
Phase: Commensurate (lock-in)
Frenkel-Kontorova Model: H = Σ[g/2·(u_{n+1}−u_n−a₀)² + K/2·(1−cos(2πu_n))]. The competition between atomic spacing a₀ and substrate period (=1) drives a commensurate-incommensurate (C-IC) transition. At exact rational ratios p/q, atoms lock in (Aubry transition). Incommensurate states host topological defects — kinks (solitons) that carry structural misfit. The ground-state winding number traces the devil's staircase as a₀ varies.