A central limit theorem for a localized version of the SK model

Sergio de Carvalho Bezerra (1) , Samy Tindel (1)

1 IECN - Institut Élie Cartan de Nancy

In this note, we consider a SK (Sherrington--Kirkpatrick)-type model on Z^d for d greater or equal to 1, weighted by a function allowing to any single spin to interact with a small proportion of the other ones. In the thermodynamical limit, we investigate the equivalence of this model with the usual SK spin system, through the study of the fluctuations of the free energy.

Mots clés: spin glasses; Sherrington-Kirkpatrick; localized mean-field model; cavity method; stochastic calculus

Domaines: Probabilités [math.PR]

Sergio de Carvalho Bezerra, Samy Tindel. A central limit theorem for a localized version of the SK model. Potential Analysis, 2007, 26, pp.323-343. ⟨10.1007/s11118-007-9041-9⟩. ⟨hal-00101520⟩