Multiscale analysis of hierarchical landscapes

The Statistical Mechanics calculation of the Gibbs-Boltzmann partition function does not give all the necessary information for a complete analysis of a rugged energy hypersurface. We show instead, that the partition function of a conveniently defined system composed of a number of replicas constrai...

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Bibliographic Details
Published in:Physica. D 1997-09, Vol.107 (2), p.151-155
Main Authors: Baviera, R., Virasoro, M.A.
Format: Article
Language:English
Subjects:
Gibbs-Boltzmann partition function
Hierarchical landscapes
Multiscale analysis
Replica formalism
Rugged energy hypersurface
TAP solutions
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Summary:The Statistical Mechanics calculation of the Gibbs-Boltzmann partition function does not give all the necessary information for a complete analysis of a rugged energy hypersurface. We show instead, that the partition function of a conveniently defined system composed of a number of replicas constrained to lie at specific distances provides such a description. We further sketch how the usual Replica formalism can be used to calculate these more complicated functions. As a by-product we show that in this way unstable solutions in the usual Replica method acquire a new meaning.
ISSN:0167-2789
1872-8022
DOI:10.1016/S0167-2789(97)00079-1