Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Mean-field theory for a spin-glass model of neural networks: TAP free
  energy and paramagnetic to spin-glass transition   An approach is proposed to the Hopfield model where the mean-field treatment
is made for a given set of stored patterns (sample) and then the statistical
average over samples is taken. This corresponds to the approach made by
Thouless, Anderson and Palmer (TAP) to the infinite-range model of spin
glasses. Taking into account the fact that in the Hopfield model there exist
correlations between different elements of the interaction matrix, we obtain
its TAP free energy explicitly, which consists of a series of terms exhibiting
the cluster effect. Nature of the spin-glass transition in the model is also
examined and compared with those given by the replica method as well as the
cavity method.

16
The categories of this paper are: stat
22
The categories of this paper are: chao-dyn
30
The categories of this paper are: q-alg
33
The categories of this paper are: plasm-ph
31
The categories of this paper are: ao-sci
21
The categories of this paper are: adap-org
28
The categories of this paper are: alg-geom
19
The categories of this paper are: eess
3
The categories of this paper are: physics
34
The categories of this paper are: chem-ph
24
The categories of this paper are: dg-ga
36
The categories of this paper are: cmp-lg
0
The categories of this paper are: hep-ph
18
The categories of this paper are: econ
15
The categories of this paper are: nucl-ex
6
The categories of this paper are: astro-ph