Crossover between special and ordinary transitions in random semi-infinite Ising-like systems

We investigate the crossover behavior between special and ordinary surface transitions in three-dimensional semi-infinite Ising-like systems with random quenched bulk disorder. We calculate the surface crossover critical exponent $\mathrm{\Phi }$, the critical exponents of the layer, ${\alpha }_1$, and local specific heats, ${\alpha }_{11}$, by applying the field theoretic approach directly in three spatial dimensions ($d=3$) up to the two-loop approximation. The numerical estimates of the resulting two-loop series expansions for the surface critical exponents are computed by means of Pad'e and Pad'e-Borel resummation techniques. We find that $\mathrm{\Phi }$, ${\alpha }_1$, ${\alpha }_{11}$ obtained in the present paper are different from their counterparts of pure Ising systems. The obtained results confirm that in a system with random quenched bulk disorder the plane boundary is characterized by a new set of critical exponents.