  We provide a self-contained account of the B vs. H constitutive relation near
H_c1 in Type II superconductors with various types of quenched random disorder.
The traditional Abrikosov result B ~ [ln (H - H_c1)]^{-2}, valid in the absence
of disorder and thermal fluctuations, changes significantly in the presence of
disorder. Moreover, the constitutive relations will depend strongly on the type
of disorder. In the presence of point disorder, B ~ (H - H_c1)^{3/2} in
three-dimensional (thick) superconductors, as shown by Nattermann and Lipowsky.
In two-dimensional (thin film) superconductors with point disorder, B ~ (H -
H_c1). In the presence of parallel columnar disorder, we find that B ~ exp[-C /
(H - H_c1)] in three dimensions, while B ~ exp[-K / (H - H_c1)^{1/2}] in two
dimensions. In the presence of nearly isotropically splayed disorder, we find
that B ~ (H - H_c1)^{3/2} in both two and three dimensions.
