  Finite-size scaling above the upper critical dimension is a long-standing
puzzle in the field of Statistical Physics. Even for pure systems various
scaling theories have been suggested, partially corroborated by numerical
simulations. In the present manuscript we address this problem in the even more
complicated case of disordered systems. In particular, we investigate the
scaling behavior of the random-field Ising model at dimension $D = 7$, i.e.,
above its upper critical dimension $D_{\rm u} = 6$, by employing extensive
ground-state numerical simulations. Our results confirm the hypothesis that at
dimensions $D > D_{\rm u}$, linear length scale $L$ should be replaced in
finite-size scaling expressions by the effective scale $L_{\rm eff} = L^{D /
D_{\rm u}}$. Via a fitted version of the quotients method that takes this
modification, but also subleading scaling corrections into account, we compute
the critical point of the transition for Gaussian random fields and provide
estimates for the full set of critical exponents. Thus, our analysis indicates
that this modified version of finite-size scaling is successful also in the
context of the random-field problem.
