Critical behavior of semi-infinite random systems at the special surface transition.

We use a three-dimensional massive field theory up to the two-loop approximation to study the critical behavior of semi-infinite quenched random Ising-like systems at the special surface transition. Besides, we extend up to the next-to leading order, the previous first-order results of the sqrt[epsilon] expansion obtained by Ohno and Okabe [Phys. Rev. B 46, 5917 (1992)]. The numerical estimates for surface critical exponents in both cases are computed by means of the Padé analysis. Moreover, in the case of the massive field theory we perform Padé-Borel resummation of the resulting two-loop series expansions for surface critical exponents. The most reliable estimates for critical exponents of semi-infinite systems with quenched bulk randomness at the special surface transition, which we can obtain in the frames of the present approximation scheme, are eta(//)=-0.238, Delta(1)=1.098, eta( perpendicular )=-0.104, beta(1)=0.258, gamma(11)=0.839, gamma(1)=1.426, delta(1)=6.521, and delta(11)=4.249. These values are different from critical exponents for pure semi-infinite Ising-like systems and show that in a system with quenched bulk randomness the plane boundary is characterized by a new set of critical exponents at the special surface transition.