Depinning transition of a directed polymer by a periodic potential: a   d-dimensional solution
  We study the depinning phase transition of a directed polymer in a $d$-dimensional space by a periodic potential localized on a straight line. We give exact formulas in all dimensions for the critical pinning we need to localize the polymer. We show that a bounded state can still arise even if, in average, the potential layer is not attractive and for diverging values of the potential on the repulsive sites. The phase transition is of second order. 
S. Galluccio and R. Graber (Institut de Physique The'orique,   Universite' de Fribourg, Switzerland)