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.
A Multi-scale Spin-Glass Mean-Field Model / Contucci, Pierluigi; Mingione, Emanuele. - In: COMMUNICATIONS IN MATHEMATICAL PHYSICS. - ISSN 0010-3616. - STAMPA. - 368:3(2019), pp. 1323-1344. [10.1007/s00220-019-03308-8]
A Multi-scale Spin-Glass Mean-Field Model
Contucci, Pierluigi
;Mingione, Emanuele
2019
Abstract
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.| File | Dimensione | Formato | |
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