Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Free energy of bipartite Sherrington-Kirkpatrick model   In this paper we study the bipartite version of Sherrington-Kirkpatrick
model. We prove that the free energy density is given by an analogue of the
Parisi formula, that contains both the usual overlap and an additional new type
of overlap. Following Panchenko, we prove the upper bound of the formula by
Guerra's replica symmetry breaking interpolation, then the matching lower bound
by Ghirlanda-Guerra identities and the Aizenman-Sims-Starr scheme. Based on
this result we study the stability of the replica symmetric solution. A new
phase exhibiting partial replica symmetry breaking is observed, where the
broken phase is realized in the larger group only.

3
The categories of this paper are: physics
35
The categories of this paper are: mtrl-th
14
The categories of this paper are: math-ph
33
The categories of this paper are: plasm-ph
23
The categories of this paper are: solv-int
1
The categories of this paper are: cs
28
The categories of this paper are: alg-geom
2
The categories of this paper are: math
27
The categories of this paper are: comp-gas
22
The categories of this paper are: chao-dyn
0
The categories of this paper are: hep-ph
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The categories of this paper are: hep-lat
36
The categories of this paper are: cmp-lg
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The categories of this paper are: gr-qc
34
The categories of this paper are: chem-ph
20
The categories of this paper are: acc-phys