Quantum Hopfield Model

Details Quantum Hopfield Model Quantum Hopfield Model

1995-12-21

arxiv.org/abs/cond-mat/9512142v2

Physics

Condensed Matter

11 pages, 1 compressed/uuencoded postscript figure, revtex

Scientific paper

The Hopfield model in a transverse field is investigated in order to clarify how quantum fluctuations affect the macroscopic behavior of neural networks. Using the Trotter decomposition and the replica method, we find that the $\alpha$ (the ratio of the number of stored patterns to the system size)-$\Delta$ (the strength of the transverse field) phase diagram of this model in the ground state resembles the $\alpha$-$T$ phase diagram of the Hopfield model quantitatively, within the replica-symmetric and static approximations. This fact suggests that quantum fluctuations play quite similar roles to thermal fluctuations in neural networks as long as macroscopic properties are concerned.

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