Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: From inherent structures to pure states: some simple remarks and
  examples   The notions of pure states and inherent structures, i.e. stable
configurations against 1-spin flip are discussed. We explain why these
different concepts accidentally coincide in mean-field models with infinite
connectivity and present an exactly solvable unidimensional model where they do
not. At zero temperature pure states are to some extent related to k-spin flip
stable configurations with k going to infinity after the thermodynamical limit
has been taken. This relationship is supported by an explicit analysis of the
TAP equations and calculation of the number of pure states and k-spin flips
stable configurations in a mean-field model with finite couplings. Finally we
discuss the relevance of the concepts of pure states and inherent structures in
finite dimensional glassy systems.

11
The categories of this paper are: hep-lat
24
The categories of this paper are: dg-ga
13
The categories of this paper are: quant-ph
2
The categories of this paper are: math
20
The categories of this paper are: acc-phys
3
The categories of this paper are: physics
22
The categories of this paper are: chao-dyn
33
The categories of this paper are: plasm-ph
14
The categories of this paper are: math-ph
18
The categories of this paper are: econ
0
The categories of this paper are: hep-ph
32
The categories of this paper are: atom-ph
28
The categories of this paper are: alg-geom
29
The categories of this paper are: funct-an
36
The categories of this paper are: cmp-lg
21
The categories of this paper are: adap-org