Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Replica analysis of Franz-Parisi potential for sparse systems   We propose a method for calculating the Franz-Parisi potential for spin glass
models on sparse random graphs using the replica method under the replica
symmetric ansatz. The resulting self-consistent equations have the solution
with the characteristic structure of multi-body overlaps, and the
self-consistent equations under this solution are equivalent to the one-step
replica symmetry breaking (1RSB) cavity equation with Parisi parameter $x=1$.
This method is useful for the evaluation of transition temperatures of the
$p$-spin model on regular random graphs under a uniform magnetic field.

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The categories of this paper are: bayes-an
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The categories of this paper are: q-bio
3
The categories of this paper are: physics
31
The categories of this paper are: ao-sci
1
The categories of this paper are: cs
6
The categories of this paper are: astro-ph
5
The categories of this paper are: gr-qc
18
The categories of this paper are: econ
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The categories of this paper are: hep-ex
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The categories of this paper are: adap-org
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The categories of this paper are: nucl-th
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The categories of this paper are: q-fin
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The categories of this paper are: hep-ph
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The categories of this paper are: math-ph
9
The categories of this paper are: nlin
33
The categories of this paper are: plasm-ph