Ultrametricity in an Inhomogeneous Simplest Spin Glass Model

摘要

The limits of validity of ultrametricity are studied. A system composed of two SKmodels weakly coupled among themselves is considered. It is assumed that each one of them separately obeys ultrametricity while it is an open question whether the relevant configurations of the total system intended as a whole can be so classified. For zero coupling the answer is trivially negative. For arbitarily small interaction energy, an analysis of the associated generalized random energy models suggests that ultrametricity is recovered. The distribution of the thermodynamical states, in mean field models in inhomogeneous spin glasses, showed that the ultrametric organization of the states is uneffected by inhomogeneity. In the replica formalism, the maximization of the correlations between the states of the two systems is observed. It is possible to introduce an additional interaction term in the replicated hamiltonian so as to decrease this kind of correlation.