Replica symmetry breaking and the nature of the spin glass phase

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 the thermodynamic limit, and we study its distribution. We also show that the space of states has an ultrametric topology Etude d'une distribution de probabilite, proposee recemment, comme parametre d'onde pour les verres de spin: la probabilite depend de la realisation particuliere des couplages, meme a la limite thermodynamique. Etude de la distribution de cette probabilite. Mise en evidence de la topologie ultrametrique de l'espace des etats