Abstract
We analyse the eigenvalue structure of the replicated transfer matrix of one-dimensional disordered Ising models. In the limit of n → 0 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 (ρ = 0). The other "replica symmetry broken" representations (ρ ≠ 0) are physically meaningful, since their largest eigenvalues λ(ρ) control the disorder-averaged moments ⟨⟨(⟨SiSj⟩ − ⟨Si⟩⟨Sj⟩)ρ⟩⟩ ∝ (λ(ρ))|i − j| of the connected two-point correlations.