REPLICA SYMMETRY-BREAKING IN ZERO DIMENSION

Authors
Citation
A. Engel, REPLICA SYMMETRY-BREAKING IN ZERO DIMENSION, Nuclear physics. B, 410(3), 1993, pp. 617-646
Citations number
27
Language
INGLESE
art.tipo
Article
Categorie Soggetti
Physics, Nuclear
Journal title
ISSN journal
0550-3213
Volume
410
Issue
3
Year of publication
1993
Pages
617 - 646
Database
ISI
SICI code
0550-3213(1993)410:3<617:RSIZD>2.0.ZU;2-A
Abstract
A simple zero-dimensional model of a disordered system is studied by m eans of a variational principle for the replicated partition function. The replica symmetric ansatz for the solution of the variational equa tions gives correct results down to zero temperature if the hamiltonia n possesses typically one minimum only. In the complementary case of m any metastable states this ansatz as well as a perturbative treatment fail at low temperature. Breaking the symmetry between the replicas in a way known from the mean-field theory of spin glasses one arrives at a consistent description of the low-temperature phase also in the pre sence of many local minima of the hamiltonian. The results compare wel l with a scaling analysis and numerical simulations. Because of its si mplicity the model may also serve as a pedagogical introduction into t he use and the meaning of replica symmetry breaking.