  The ferromagnet-to-paramagnet transition of the four-dimensional random-field
Ising model with Gaussian distribution of the random fields is studied. Exact
ground states of systems with sizes up to 32^4 are obtained using graph
theoretical algorithms. The magnetization, the disconnected susceptibility, the
susceptibility and a specific heat-like quantity are calculated. Using
finite-size scaling techniques, the corresponding critical exponents are
obtained: \beta=0.15(6), \gamma`=3.12(10), \gamma=1.57(10) and \alpha=0
(logarithmic divergence). Furthermore, values for the critical randomness
h_c=4.18(1) and the correlation-length exponent \nu=0.78(10) were found. These
independently obtained exponents are compatible with all (hyper-) scaling
relations and support the two-exponent scenario (\gamma`=2\gamma)
