| Issue |
Europhys. Lett.
Volume 36, Number 3, October III 1996
|
|
|---|---|---|
| Page(s) | 209 - 214 | |
| Section | Condensed matter: electronic structure, electrical, magnetic and optical properties | |
| DOI | https://doi.org/10.1209/epl/i1996-00212-8 | |
| Published online | 01 September 2002 | |
Replica structure of one-dimensional disordered Ising models
1
Institut für Theoretische Physik, Otto-von-Guericke-Universität Magdeburg,
PSF 4120, 39016
Magdeburg, Germany
2
CNRS-Laboratoire de Physique Théorique de l'Ecole Normale
Supérieure, 24 rue
Lhomond, 75231 Paris cedex 05, France
Received:
17
May
1996
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
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