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: β1 for the surface layer magnetization and the surface excess exponents for the magnetization and the specific heat, βs and αs. 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 θ as in the bulk. The boundary disorders faster than the bulk, and the experimental and theoretical implications are discussed.