The fixed point attractor naturally follows from the Hopfield network.
The Hopfield memory model has an early memory saturation point before which memory retrieval drastically slows and becomes unreliable.
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Gibbs measure implies the Markov property (a certain kind of statistical independence); and importantly, it implies the Hammersley–Clifford theorem that the energy function can be written as a multiplication of parts, thus leading to its widespread appearance in many problems outside of physics, such as Hopfield networks, Markov networks, and Markov logic networks.