Universality of surface critical behavior of the three-dimensional Ising model in a random surface field.

Abstract

The Harris criterion is generalized to determine the relevance at bulk criticality (in the scaling theory sense) of a random ordering field acting at a surface only. For surface critical behavior of the three-dimensional Ising model the criterion predicts the random field to be irrelevant for the ordinary transition, and relevant for the surface-bulk multicritical point. Monte Carlo results for the ordinary transition verify the prediction. Moreover, surface critical behavior near substrates chemically altered in part, as used in a series of experiments by Franck and co-workers, is in the universality class mentioned above, and the value of ${\ensuremath{\beta}}_{1}$ found in a random surface experiment [D. J. Durian, and C. Franck, Phys. Rev. Lett. 59, 555 (1987)] agrees with the scaling prediction.