  We investigate the low temperature asymptotics and the finite size spectrum
of a class of Temperley-Lieb models. As reference system we use the spin-1/2
Heisenberg chain with anisotropy parameter $\Delta$ and twisted boundary
conditions. Special emphasis is placed on the study of logarithmic corrections
appearing in the case of $\Delta=1/2$ in the bulk susceptibility data and in
the low-energy spectrum yielding the conformal dimensions. For the $sl(2|1)$
invariant 3-state representation of the Temperley-Lieb algebra with
$\Delta=1/2$ we give the complete set of scaling dimensions which show huge
degeneracies.
