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We study the Hopfield model where the ratio $\alpha$ of patterns to sitesgrows large. We prove that the free energy with inverse temperature $\beta$ andexternal field $B$ behaves like $\beta\sqrt\alpha+\gamma$, where $\gamma$ isthe limiting free energy of the Sherrington-Kirkpatrick model with inversetemperature $\sqrt2\beta$ and external field $B$.

The Hopfield Model with Superlinearly Many Patterns