Rare-event induced binding transition of heteropolymers

Sequence heterogeneity broadens the binding transition of a polymer onto a linear or planar substrate. This effect is analyzed in a real-space renormalization group scheme designed to capture the statistics of rare events. In the strongly disordered regime, binding initiates at an exponentially rare set of "good contacts." Renormalization of the contact potential yields a Kosterlitz--Thouless-type transition in any dimension. This and other predictions are confirmed by extensive numerical simulations of a directed polymer interacting with a columnar defect.