SCALING EXPONENTS AT THE TRANSITION BY BREAKING OF ANALYTICITY FOR INCOMMENSURATE STRUCTURES

A wide class of solid-state models support incommensurate structures. They are mostly given by either an analytic function in which case they are free to slide, or a discontinuous function in which case there is a non-zero minimum force required for depinning and a non-zero minimum phonon frequency. I propose that the boundary between these two types of state is given at least in part by the stable manifold of a fixed point of a renormalisation operator. This permits one to predict scaling laws for the depinning force, phonon gap, elasticity, effective mass and other quantities