Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Role of the Finite Replica Analysis in the Mean-Field Theory of Spin
  Glasses   In this thesis, we review and examine the replica method from several
viewpoints. The replica method is a mathematical technique to calculate general
moments of stochastic variables. This method provides a systematic way to
evaluate physical quantities and becomes one of the most important tools in the
theory of spin glasses and in the related discipline including information
processing tasks.
  In spite of the effectiveness of the replica method, it is known that several
problems exist in the procedures of the method itself. The replica symmetry
breaking is the central topic of those problems and is the main issue of this
thesis. To elucidate this point, we review the recent progress about the
replica symmetry breaking including its physical and mathematical descriptions
in detail.
  Based on those descriptions, several spin-glass models and Ising perceptron
are deeply investigated.

19
The categories of this paper are: eess
28
The categories of this paper are: alg-geom
11
The categories of this paper are: hep-lat
30
The categories of this paper are: q-alg
27
The categories of this paper are: comp-gas
10
The categories of this paper are: q-bio
26
The categories of this paper are: bayes-an
22
The categories of this paper are: chao-dyn
35
The categories of this paper are: mtrl-th
1
The categories of this paper are: cs
12
The categories of this paper are: nucl-th
34
The categories of this paper are: chem-ph
5
The categories of this paper are: gr-qc
36
The categories of this paper are: cmp-lg
31
The categories of this paper are: ao-sci
18
The categories of this paper are: econ