We show that given certain plausible assumptions the existence of persistent states in a neural network can occur only if a certain transfer matrix has degenerate maximum eigenvalues. The existence of such states of persistent order is directly analogous to the existence of long range order in an Ising spin system; while the transition to the state of persistent order is analogous to the transition to the ordered phase of the spin system. It is shown that the persistent state is also characterized by correlations between neurons throughout the brain. It is suggested that these persistent states are associated with short term memory while the eigenvectors of the transfer matrix are a representation of long term memory. A numerical example is given that illustrates certain of these features.
[1]
A. Hodgkin,et al.
Action Potentials Recorded from Inside a Nerve Fibre
,
1939,
Nature.
[2]
E. N. Lassettre,et al.
Thermodynamic Properties of Binary Solid Solutions on the Basis of the Nearest Neighbor Approximation
,
1941
.
[3]
H. Kramers,et al.
Statistics of the Two-Dimensional Ferromagnet. Part II
,
1941
.
[4]
W. E. Lamb,et al.
The Propagation of Order in Crystal Lattices
,
1943
.
[5]
T. D. Lee,et al.
Statistical Theory of Equations of State and Phase Transitions. II. Lattice Gas and Ising Model
,
1952
.
[6]
G. F. Newell,et al.
On the Theory of the Ising Model of Ferromagnetism
,
1953
.
[7]
A. Messiah.
Quantum Mechanics
,
1961
.
[8]
C. Smith,et al.
The brain
,
1970
.