Multi-species mean-field spin-glasses. Rigorous results

Understand

We study a multi-species spin glass system where the density of each species is kept fixed at increasing volumes.

• The model reduces to the Sherrington-Kirkpatrick one for the single species case.
• The existence of the thermodynamic limit is proved for all densities values under a convexity condition on the interaction.
• The thermodynamic properties of the model are investigated and the annealed, the replica symmetric and the replica symmetry breaking bounds are proved using Guerra's scheme.