  We consider the properties of $T=0$ quantum phases of matter - especially
superconducting and analogous spin-liquid phases - on infinite cylinders of
width $L_\perp$ and analyze the ways in which the $L_\perp \to \infty$ (2d)
limit is approached. This problem is interesting in its own right, but is
particularly important in the context of extrapolating accessible density
matrix renormalization group (DMRG) results on model strongly interacting
problems to the desired 2d limit. Various methods for drawing firm conclusions
about the quantum phases in 2d from relatively small $L_{\perp}$ results are
illustrated.
