EXACTLY SOLVED FRENKEL-KONTOROVA MODEL - ALMOST EVERYWHERE CONCAVE POTENTIAL

We solved the Frenkel-Kontorova model with the potential V(u) = -lambd a(u - Int[u] - 1/2)(2)/2 exactly. The minimum energy configurations an d recurrent configurations with fixed winding number are completely ch aracterized. The average energy per atom of different configurations a re explicitly calculated, which is used to determine the ground state configuration with a given winding number. The evolution of the ground state configurations is shown to be dictated by the Farey fractions.