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In this paper we investigate the spectrum of $OSp(n|2m)$ quantum spin chainswith free boundary conditions. We compute the surface free energy of thesemodels which, similar to other properties in the thermodynamic limit includingthe effective central charge of the underlying conformal field theory, dependson $n-2m$ only. For several models in the regime $n-2m< 2$ we have studied thefinite-size properties including the subleading logarithmic corrections toscaling. As in the case of periodic boundary conditions we find the existenceof a tower of states with the same conformal dimension as the identityoperator. As expected the amplitudes of the corresponding logarithmiccorrections differ from those found previously for the models with periodicboundary conditions. We point out however the existence of simple relationsconnecting such amplitudes for free and periodic boundaries. Based on ourfindings we formulate a conjecture on the long distance behaviour of the bulkand surface watermelon correlators.

$OSp(n|2m)$ quantum chains with free boundaries