  We investigate the application of graph-cut methods for the study of the
critical behaviour of the two-dimensional random-field Ising model. We focus on
exact ground-state calculations, crossing the phase boundary of the model at
zero temperature and varying the disorder strength. For this purpose we employ
two different minimum-cut--maximum-flow algorithms, one of augmenting-path and
another of push-relabel style. We implement these approaches for the square and
triangular lattice problems and compare their computational efficiency.
