Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The full replica symmetry breaking solution in mean-field spin glass
  models   This thesis focus on the extension of the Parisi full replica symmetry
breaking solution to the Ising spin glass on a random regular graph. We propose
a new martingale approach, that overcomes the limits of the Parisi-M\'ezard
cavity method, providing a well-defined formulation of the full replica
symmetry breaking problem in random regular graphs. We obtain a variational
free energy functional, defined by the sum of two variational functionals
(auxiliary variational functionals), that are an extension of the Parisi
functional of the Sherrington-Kirkpatrick model. We study the properties of the
two variational functionals in detailed, providing representation through the
solution of a proper backward stochastic differential equation, that generalize
the Parisi partial differential equation. Finally, we define the order
parameters of the system and get a set of self-consistency equations for the
order parameters and free energy.

7
The categories of this paper are: hep-th
21
The categories of this paper are: adap-org
30
The categories of this paper are: q-alg
0
The categories of this paper are: hep-ph
29
The categories of this paper are: funct-an
36
The categories of this paper are: cmp-lg
28
The categories of this paper are: alg-geom
5
The categories of this paper are: gr-qc
22
The categories of this paper are: chao-dyn
14
The categories of this paper are: math-ph
12
The categories of this paper are: nucl-th
17
The categories of this paper are: q-fin
23
The categories of this paper are: solv-int
6
The categories of this paper are: astro-ph
31
The categories of this paper are: ao-sci
3
The categories of this paper are: physics