Ground-States of Two Directed Polymers
  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. 
V. T. Petaja, M. J. Alava, and H. Rieger