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

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.