Abstract
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.
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