2001/05/31 by Shinsuke Koyama
Computer Science · Neuroscience · Physics and Astronomy · #Neural Networks and Applications #Neural dynamics and brain function #Theoretical and Computational Physics #cond-mat.dis-nn
paper · pdf · doi:10.1103/physreve.65.016124
13pages, 7figures, revtex4
arxiv created 2001/08/10 · openalex publication_date 2001/12/19 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We investigate the maximum number of embedded patterns in the two-dimensional Hopfield model. The grand state energies of two specific network states, namely, the energies of the pure-ferromagnetic state and the state of specific one stored pattern are calculated exactly in terms of the correlation function of the ferromagnetic Ising model. We also investigate the energy landscape around them and the stability of the pure retrieval state. Taking into account the qualitative features of the phase diagrams obtained by Nishimori, Whyte, and Sherrington [Phys. Rev. E 51, 3628 (1995)], we conclude that the network cannot retrieve more than three patterns.