Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Legendre structure of the Parisi formula   We show that the Parisi formula of the mixed $p$-spin model is a concave
function of the squared inverse temperature. This allows us to derive a new
expression for the Parisi formula that involves the inverse temperature and the
Parisi measure as Legendre conjugate variables.

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The categories of this paper are: hep-ph
16
The categories of this paper are: stat
19
The categories of this paper are: eess
36
The categories of this paper are: cmp-lg
24
The categories of this paper are: dg-ga
6
The categories of this paper are: astro-ph
34
The categories of this paper are: chem-ph
25
The categories of this paper are: patt-sol
13
The categories of this paper are: quant-ph
10
The categories of this paper are: q-bio
21
The categories of this paper are: adap-org
29
The categories of this paper are: funct-an
31
The categories of this paper are: ao-sci
12
The categories of this paper are: nucl-th
30
The categories of this paper are: q-alg
5
The categories of this paper are: gr-qc