Defectibility and frustration in incommensurate structures: The devil's stair case transformation

I. DEFECTIBILITY AND FRUSTRATION-GENERAL IDEAS Frustration is a concept which has been initially introduced for spin-glasses1 which can be simply generalised to many other situations. A system is called frustrated if these exists conflicting forces between the atoms, spins etc. of this system, each of which would propose a different structure. This concept is useful when it is associated with the concept of defectibility: if the system is sufficiently elastic or quasi-elastic, the resulting structure varies continuously with the relative conflicting forces and this concept is useless, But when the system configuration evolves by local defect creations* (or annihilation) its transformation becomes locally discontinuous which results in a qualitative different macroscopic behavior** (e.g the devil's stair case). The aim of this paper is to show on a crude model for phase transitions in incommensurate structures, that defectibility and frustration involves spontaneously mathematical pathologies which have a physical interpretation and can be useful to shed some light on unexplained experiments2.