Solving spin systems: the Babylonian way

2021/11/08 by Kistler, Nicola
#FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR)

paper · doi:10.48550/arxiv.2111.04375

Abstract

We show that spin systems with generic (ferro- or paramagnetic, or random) interactions are "completely integrable". The approach is worked out, by way of example, for the Sherrington Kirkpatrick model: we derive an exact, closed formula for the quenched free energy in finite volume which involves an integral over a Gaussian field with correlation structure given by the interaction matrix (with a twist).

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