Solving spin systems: the Babylonian way

TL;DR

This paper demonstrates that general spin systems, including complex models like the Sherrington Kirkpatrick model, are completely integrable, providing exact formulas for their free energy using a novel approach involving Gaussian integrals.

Contribution

It introduces a new method to exactly solve spin systems with generic interactions, extending integrability to complex models like SK.

Findings

Derived an exact formula for the quenched free energy of the SK model.

Established the integrability of a broad class of spin systems.

Connected free energy calculations to Gaussian field integrals.

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).