An approach to chaos in some mixed -spin models

We consider the problems of chaos in disorder and temperature for coupled copies of the mixed -spin models. Under certain assumptions on the parameters of the models, first we prove a weak form of chaos by showing that the overlap is concentrated around its Gibbs average depending on the disorder an...

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Bibliographic Details
Published inProbability theory and related fields Vol. 157; no. 1-2; pp. 389 - 404
Main Authors Chen, Wei-Kuo, Panchenko, Dmitry
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.10.2013
Springer Nature B.V
Subjects
Economics
Finance
Insurance
Management
Mathematical and Computational Biology
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Probability
Probability Theory and Stochastic Processes
Quantitative Finance
Statistics for Business
Theoretical
Chaos
Stability
82B44
Spin glass models
60K35
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Summary:We consider the problems of chaos in disorder and temperature for coupled copies of the mixed -spin models. Under certain assumptions on the parameters of the models, first we prove a weak form of chaos by showing that the overlap is concentrated around its Gibbs average depending on the disorder and then obtain several results toward strong chaos by providing control of the overlap between two systems in terms of their Parisi measures.
ISSN:0178-8051
1432-2064
DOI:10.1007/s00440-012-0460-1