Surface criticality in random field magnets

Abstract

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: $\beta_1$ for the surface layer magnetization and the surface excess exponents for the magnetization and the specific heat, $\beta_s$ and $\alpha_s$. The latter ones are related to the bulk phase transition by the same scaling laws as in pure systems, but only with the same violation of hyperscaling exponent $\theta$ as in the bulk. The boundary disorders faster than the bulk, and the experimental and theoretical implications are discussed.