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

Mathematics – Probability

Scientific paper

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22 pages

Scientific paper

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.

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