Surface criticality in random field magnets

The boundary-induced scaling of three-dimensional random field Ising magnets is investigated close to the bulk critical point by exact combinatorial optimization methods. We measure several exponents describing surface criticality: ${\ensuremath{\beta}}_{1}$ for the surface layer magnetization and the surface excess exponents for the magnetization and the specific heat, ${\ensuremath{\beta}}_{s}$ and ${\ensuremath{\alpha}}_{s}$. The latter are related to the bulk phase transition by the same scaling laws as in pure systems, but only with the same violation of the hyperscaling exponent $\ensuremath{\theta}$ as in the bulk. The boundary disorders faster than the bulk, and the experimental and theoretical implications are discussed.