This book contains a detailed and self-contained presentation of the replica theory of infinite range spin glasses. The authors also explain recent theoretical developments, paying particular… Expand

Ultrametricity is a simple topological concept, but its appearance in the language of physicists is recent. This review provides all the elementary background (from mathematics, taxonomy, and… Expand

A probability distribution has been proposed recently by one of us as an order parameter for spin glasses. We show that this probability depends on the particular realization of the couplings even in… Expand

The hierarchical organization of the pure states of a S.K. spin glass (ultrametricity) is analysed in terms of self-averaging distributions of local magnetizations. We show that every pure state α… Expand

A new method is introduced, which does not use replicas, from which all the results of the replica symmetry-breaking solution of the Sherrington-Kirkpatrick model are recovered.Expand

The free energies of the pure states in the spin glass phase are studied in the mean field theory. They are shown to be independent random variables with an exponential distribution. Physical… Expand