  We study the spin stiffness of a one-dimensional quantum antiferromagnet in
the whole range of system sizes $L$ and temperatures $T$. We show that for
integer and half-odd integer spin case the stiffness differs fundamentally in
its $L$ and $T$ dependence, and that in the latter case the stiffness exhibits
a striking dependence on the parity of the number of sites. Integer spin chains
are treated in terms of the non-linear sigma model, while half-odd integer spin
chains are discussed in a renormalization group approach leading to a Luttinger
liquid with Aharonov-Bohm type boundary conditions.
