  Joint ground states of two directed polymers in a random medium are
investigated. Using exact min-cost flow optimization the true two-line
ground-state is compared with the single line ground state plus its first
excited state. It is found that these two-line configurations are (for almost
all disorder configurations) distinct implying that the true two-line
ground-state is non-separable, even with 'worst-possible' initial conditions.
The effective interaction energy between the two lines scales with the system
size with the scaling exponents 0.39 and 0.21 in 2D and 3D, respectively.
