  We present a semiclassical theory of weak disorder effects in small
structures and apply it to the magnetic response of non-interacting electrons
confined in integrable geometries. We discuss the various averaging procedures
describing different experimental situations in terms of one- and two-particle
Green functions. We demonstrate that the anomalously large zero-field
susceptibility characteristic of clean integrable structures is only weakly
suppressed by disorder. This damping depends on the ratio of the typical size
of the structure with the two characteristic length scales describing the
disorder (elastic mean-free-path and correlation length of the potential) in a
power-law form for the experimentally relevant parameter region. We establish
the comparison with the available experimental data and we extend the study of
the interplay between disorder and integrability to finite magnetic fields.
