  We investigate the effect of quenched surface disorder on effective
interactions between two planar surfaces immersed in fluids which are near
criticality and belong to the Ising bulk universality class. We consider the
case that, in the absence of random surface fields, the surfaces of the film
belong to the surface universality class of the so-called ordinary transition.
We find analytically that in the linear weak-coupling regime, i.e., upon
including the mean-field contribution and Gaussian fluctuations, the presence
of random surface fields with zero mean leads to an attractive,
disorder-induced contribution to the critical Casimir interactions between the
two confining surfaces. Our analytical, field-theoretic results are compared
with corresponding Monte Carlo simulation data.
