[Submitted on 12 Jan 2026 (v1), last revised 21 Jul 2026 (this version, v3)]

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Abstract:The Hopfield model, originally inspired by spin glasses, occupies a central place at the intersection of statistical mechanics, neural networks, and artificial intelligence. Despite its conceptual simplicity and broad applicability, it is rarely integrated into the undergraduate physics curriculum. We present the Hopfield model as a pedagogically rich framework that naturally unifies core topics from the undergraduate physics curriculum and that provides a concise introduction based on concepts such as a model's energy function, dynamics, and pattern stability. We discuss practical aspects of its simulation and provide simulation codes. We also propose problems designed to mirror research practice, which can be included in undergraduate classes.

Submission history

From: Mauricio Girardi-Schappo [view email]
[v1] Mon, 12 Jan 2026 15:16:15 UTC (2,886 KB)
[v2] Wed, 14 Jan 2026 13:36:51 UTC (2,886 KB)
[v3] Tue, 21 Jul 2026 20:44:15 UTC (3,331 KB)