  We consider a classical random-bond Ising model (RBIM) with binary
distribution of $\pm K$ bonds on the square lattice at finite temperature. In
the phase diagram of this model there is the so-called Nishimori line which
intersects the phase boundary at a multicritical point. It is known that the
correlation functions obey many exact identities on this line. We use a
supersymmetry method to treat the disorder. In this approach the transfer
matrices of the model on the Nishimori line have an enhanced supersymmetry
osp($2n+1|2n$), in contrast to the rest of the phase diagram, where the
symmetry is osp($2n|2n$) (where $n$ is an arbitrary positive integer). An
anisotropic limit of the model leads to a one-dimensional quantum Hamiltonian
describing a chain of interacting superspins, which are irreducible
representations of the osp($2n+1|2n$) superalgebra. By generalizing this
superspin chain, we embed it into a wider class of models. These include other
models that have been studied previously in one and two dimensions. We suggest
that the multicritical behavior in two dimensions of a class of these
generalized models (possibly not including the multicritical point in the RBIM
itself) may be governed by a single fixed point, at which the supersymmetry is
enhanced still further to osp($2n+2|2n$). This suggestion is supported by a
calculation of the renormalization-group flows for the corresponding nonlinear
sigma models at weak coupling.
