Universal scaling limits for spin networks via martingale methods

Abstract

We use simple martingale methods to construct a large deviation theory of spin systems with pairwise interactions. As an application, we show that the fully connected case obeys a universal scaling limit that is just a product of magnetisation eigenstates.

Respect to the published version: a star is added in eq.(19) and after eq.(27) to distinguish the standard Gibbs measure from the locally normalized version. Other minor typos fixed. 25 pages, 1 figure

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