2000/07/31 by Ilya A. Gruzberg, N. Read, Andreas W. W. Ludwig · 4 citations
Mathematics · Physics and Astronomy · #Geometry #Ising model #Line (geometry) #Mathematical physics #Mathematics #Physics #Quantum many-body systems #Statistical physics #Stochastic processes and statistical mechanics #Supersymmetry #Theoretical and Computational Physics #cond-mat.dis-nn #cond-mat.mes-hall
paper · pdf · doi:10.1103/physrevb.63.104422
published as Phys. Rev. B 63, 104422 (2001). · 28 pages; largely independent of cond-mat/0007255. V. 2: small additions, references updated; as published
arxiv created 2000/12/18 · openalex publication_date 2001/02/20 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We consider a classical random-bond Ising model (RBIM) with binary distribution of \ifmmode±\else\textpm\fiK 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.