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We investigate the low temperature asymptotics and the finite size spectrumof a class of Temperley-Lieb models. As reference system we use the spin-1/2Heisenberg chain with anisotropy parameter $\Delta$ and twisted boundaryconditions. Special emphasis is placed on the study of logarithmic correctionsappearing in the case of $\Delta=1/2$ in the bulk susceptibility data and inthe 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 hugedegeneracies.

The complete conformal spectrum of a $sl(2|1)$ invariant network model and logarithmic corrections