Numerical results for the ground-state interface in a random medium

The problem of determining the ground state of a d-dimensional interface embedded in a (d+1)-dimensional random medium is treated numerically. Using a minimum-cut algorithm, the exact ground states can be found for a number of problems for which other numerical methods are inexact and slow. In particular, results are presented for the roughness exponents and ground-state energy fluctuations in a random bond Ising model. It is found that the roughness exponent ζ=0.41±0.01,0.22±0.01, with the related energy exponent being θ=0.84±0.03,1.45±0.04, in d=2,3, respectively. These results are compared with previous analytical and numerical estimates.