Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Legendre Duality of Spherical and Gaussian Spin Glasses   The classical result of concentration of the Gaussian measure on the sphere
in the limit of large dimension induces a natural duality between Gaussian and
spherical models of spin glass. We analyse the Legendre variational structure
linking the free energies of these two systems, in the spirit of the
equivalence of ensembles of statistical mechanics. Our analysis, combined with
the previous work [4], shows that such models are replica symmetric. Lastly, we
briefly discuss an application of our result to the study of the Gaussian
Hopfield model.

16
The categories of this paper are: stat
11
The categories of this paper are: hep-lat
15
The categories of this paper are: nucl-ex
24
The categories of this paper are: dg-ga
13
The categories of this paper are: quant-ph
31
The categories of this paper are: ao-sci
23
The categories of this paper are: solv-int
1
The categories of this paper are: cs
9
The categories of this paper are: nlin
34
The categories of this paper are: chem-ph
36
The categories of this paper are: cmp-lg
37
The categories of this paper are: supr-con
30
The categories of this paper are: q-alg
14
The categories of this paper are: math-ph
8
The categories of this paper are: hep-ex
32
The categories of this paper are: atom-ph