We introduce the concept of Random Multi-Overlap Structure (RaMOSt) as a generalization of the one introduced by M. Aizenman R. Sims and S. L. Starr for non-diluted spin glasses. We use such methodâ€¦ (More)

We provide a strategy to find in few elementary calculations the critical exponents of the overlaps for dilute spin glasses, in absence of external field. Such a strategy is based on the expansion ofâ€¦ (More)

We provide a systematic treatment of self-averaging identities for various spin systems. The method is quite general, basically not relying on the nature of the model, and as a special case recoversâ€¦ (More)

We prove that the Aizenman-Contucci relations, well known for fully connected spin glasses, hold in diluted spin glasses as well. We also prove more general constraints in the same spirit forâ€¦ (More)

We study the mean field dilute model of a ferromagnet. We find and prove an expression for the free energy density at high temperature, and at temperature zero. We find the critical line of theâ€¦ (More)

We investigate overlap fluctuations of the Sherrington-Kirkpatrick mean field spin glass model in the framework of the Random Overlap Structure (ROSt). The concept of ROSt has been introducedâ€¦ (More)

We extend the approach of Aizenman, Sims and Starr for the SK-type models to their spherical versions. Such an extension has already been performed for diluted spin glasses. The factorizationâ€¦ (More)

We propose an ultrametric breaking of replica symmetry for diluted spin glasses in the framework of RandomMulti-Overlap Structures (RaMOSt). Such proposal is closer to the Parisi theory forâ€¦ (More)

In this paper we derive recursively an expression for the free energy of the Sherrington-Kirkpatrick (SK) model in the framework of Random Overlap Structures (ROSt) recently introduced by Aizenmanâ€¦ (More)

We show how to determine if a given vector can be the signature of a system on a finite number of components and, if so, exhibit such a system in terms of its structure function. The method employsâ€¦ (More)