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We propose an ultrametric breaking of replica symmetry for diluted spin glasses in the framework of Random Multi-Overlap Structures (RaMOSt). Our approach permits to bound the free energy through a trial function that depends on a set of numbers over which one has to take the infimum.Such trial function is a first (ultrametric and factorized) example of a bound in the intersection of the probability spaces of the iterative and the RaMOSt theories, and it shows that a “direct dilution” of the Parisi Ansatz is not always exact.

Ultrametric Broken Replica Symmetry RaMOSt