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This paper is concerned with the investigation of the massless regime of anintegrable spin chain based on the quantum group deformation of the $OSp(3|2)$superalgebra. The finite-size properties of the eigenspectra are computed bysolving the respective Bethe ansatz equations for large system sizes allowingus to uncover the low-lying critical exponents. We present evidences thatcritical exponents appear to be built in terms of composites of anomalousdimensions of two Coulomb gases with distinct radii and the exponentsassociated to $Z(2)$ degrees of freedom. This view is supported by the factthat the $S=1$ XXZ integrable chain spectrum is present in some of the sectorsof our superspin chain at a particular value of the deformation parameter. Wefind that the fine structure of finite-size effects is very rich for a typicalanisotropic spin chain. In fact, we argue on the existence of a family ofstates with the same conformal dimension whose lattice degeneracies areapparently lifted by logarithmic corrections. On the other hand we also reporton states of the spectrum whose finite-size corrections seem to be governed bya power law behaviour. We finally observe that under toroidal boundaryconditions the ground state dependence on the twist angle has two distinctanalytical structures.

On the critical behaviour of the integrable $q$-deformed $OSp(3|2)$ superspin chain