Fermions in a random medium
  We study the continuum field theory for an ensemble of directed polymers r_i (t) in 1+d' dimensions that live in a medium with quenched point disorder and interact via short-ranged pair forces g \Psi (r_i - r_j). 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 bound state with localization length \xi_\perp \sim |g|^{-\nu_\perp}; repulsive forces lead to mutual avoidance with a pair distribution function P(r_i - r_j) \sim |r_i - r_j|^\theta reminiscent of interacting fermions. In the experimentally important dimension d' = 2, we obtain \nu_\perp \approx 0.8 and \theta \approx 2.4 . 
Harald Kinzelbach and Michael Lassig