  The equilibrium behavior of a system of elastic layers under tension in the
presence of correlated disorder is studied using functional renormalization
group techniques. The model exhibits many of the features of the Bose glass
phase of type II superconductors induced by columnar defects, but may be more
directly applicable to charge density waves, incommensurate striped magnetic
phases, stacked membranes under tension, vicinal crystal surfaces, or
superconducting ``vortex--chains''. Below five dimensions, an epsilon expansion
for the stable zero temperature fixed point yields the properties of the glassy
phase. Transverse to the direction of correlation, the randomness induces
logarithmic growth of displacements. Displacements are strongly localized in
the correlation direction. The absence of a response to a weak applied
transverse field (transverse Meissner effect) is demonstrated analytically. In
this simple model, the localized phase is stable to point disorder, in contrast
to the behavior in the presence of dislocations, in which the converse is
believed to be true.
