Exact solution and finite size properties of the $U_{q}[osp(2|2m)]$ vertex model

We have diagonalized the transfer matrix of the $U_{q}[osp(2|2m)]$ vertex model by means of the algebraic Bethe ansatz method for a variety of grading possibilities. This allowed us to investigate the thermodynamic limit as well as the finite size properties of the corresponding spin chain in the massless regime. The leading behaviour of the finite size corrections to the spectrum is conjectured for arbitrary $m$. For $m=1$ we find a critical line with central charge $c=-1$ whose exponents vary continuously with the $q$-deformation parameter. For $m\geq 2$ the finite size term related to the conformal anomaly depends on the anisotropy which indicates a multicritical behaviour typical of loop models.