Replica structure of one-dimensional disordered Ising models
Institut für Theoretische Physik, Otto-von-Guericke-Universität Magdeburg,
PSF 4120, 39016
2 CNRS-Laboratoire de Physique Théorique de l'Ecole Normale Supérieure, 24 rue Lhomond, 75231 Paris cedex 05, France
Accepted: 12 September 1996
We analyse the eigenvalue structure of the replicated transfer matrix of one-dimensional disordered Ising models. In the limit of replicas, an infinite sequence of transfer matrices is found, each corresponding to a different irreducible representation (labelled by a positive integer ρ) of the permutation group. We show that the free energy can be calculated from the replica-symmetric subspace (). The other "replica symmetry broken” representations () are physically meaningful, since their largest eigenvalues control the disorder-averaged moments of the connected two-point correlations.
PACS: 75.10.Nr – Spin-glass and other random models / 02.10.Sp – Linear and multilinear algebra; matrix theory (finite and infinite) / 05.50.+q – Lattice theory and statistics; Ising problems
© EDP Sciences, 1996