Commensurate-Incommensurate Transitions with Quenched Random Impurities

Commensurate-incommensurate transitions in uniaxial two-dimensional systems are examined in the presence of impurities that interact with domain walls. Exact Bethe-Ansatz calculations, tested by numerical studies, indicate that randomness is relevant and leads to new critical behavior---a discontinuity in the specific heat and divergence of domain size with an exponent of 1. The results are interpreted in terms of the behavior of a single interface. Global phase diagrams are presented and experimental implications are discussed.