A Multi-Scale Spin-Glass Mean-Field Model

Understand

In this paper a multi-scale version of the Sherrington and Kirkpatrick model is introduced and studied.

• The pressure per particle in the thermodynamical limit is proved to obey a variational principle of Parisi type.
• The result is achieved by means of lower and upper bounds.
• The lower bound is obtained with a Ruelle cascade using the interpolation technique, while the upper bound exploits factorisation properties of the equilibrium measure and the synchronisation technique