https://doi.org/10.1140/epjs/s11734-025-01835-1
Regular Article
Hopfield model for patterns with internal structure
Institute for Theoretical Physics, University of Amsterdam, Science Park 904, 1090 GL, Amsterdam, The Netherlands
Received:
5
May
2025
Accepted:
25
July
2025
Published online:
4
August
2025
The spherical version of the Hopfield model for pattern recognition is considered in the static limit. Structures inside the patterns are modeled by Gaussian random variables that reward correlation between pairs of spins in a given pattern. The free energy is derived analytically with the replica method. The overlap distribution obeys a self-consistent equation. Coming from high temperatures, a spin glass phase is entered, in which patterns and correlations appear at lower temperatures. For small enough loading capacity, also a glass phase with patterns and correlations appears.
© The Author(s) 2025
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