  The low energy spectrum of a spin chain with $OSp(3|2)$ supergroup symmetry
is studied based on the Bethe ansatz solution of the related vertex model. This
model is a lattice realization of intersecting loops in two dimensions with
loop fugacity $z=1$ which provides a framework to study the critical properties
of the unusual low temperature Goldstone phase of the $O(N)$ sigma model for
$N=1$ in the context of an integrable model. Our finite-size analysis provides
strong evidence for the existence of continua of scaling dimensions, the lowest
of them starting at the ground state. Based on our data we conjecture that the
so-called watermelon correlation functions decay logarithmically with exponents
related to the quadratic Casimir operator of $OSp(3|2)$. The presence of a
continuous spectrum is not affected by a change to the boundary conditions
although the density of states in the continua appears to be modified.
