We study the continuum field theory for an ensemble of directed polymers ri(t) in 1+d ′ dimensions that live in a medium with quenched point disorder and interact via short-ranged pair forces gΨ(ri − rj). In the strong-disorder (or low-temperature) regime, such forces are found to be relevant in any dimension d′ below the upper critical dimension for a single line. Attractive forces generate a ...

We develop a renormalized continuum field theory for a directed polymer interacting with a random medium and a single extended defect. The renormalization group is based on the operator algebra of the pinning potential; it has novel features due to the breakdown of hyperscaling in a random system. There is a second-order transition between a localized and a delocalized phase of the polymer; we ...

Abstract Disordered spring networks can exhibit rigidity transitions, due to either the removal of material in over-constrained or application strain under-constrained ones. While an effective medium theory (EMT) exists for former, there is none latter. We, therefore, formulate EMT random regular, with purely geometrical disorder predict their stiffness via distribution tensions. We find a line...