Random-bond Ising model in two dimensions: The Nishimori line and supersymmetry - art. no. 104422

We consider a classical random-bond Ising model (RBIM) with binary distribu tion of +/-K bonds on the square lattice at finite temperature. In the phas e diagram of this model there is the so-called Nishimori line which interse cts the phase boundary at a multicritical point. It is known that the corre lation functions obey many exact identities on this line. We use a supersym metry method to treat the disorder. In this approach the transfer matrices nf the model on the Nishimori line have an enhanced supersymmetry osp(2n+1\ 2n), in contrast to the rest of the phase diagram, when 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 chai n of interacting superspins, which are irreducible representations of the o sp(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 multicrit ical behavior in two dimensions of a class of these generalized models (pos sibly not including the multicritical point in the RBIM itself) may he gove rned 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 model s at weak coupling.