Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A note on the free energy of the coupled system in the
  Sherrington-Kirkpatrick model   In this paper we consider a system of spins that consists of two
configurations $\vsi^1,\vsi^2\in\Sigma_N=\{-1,+1\}^N$ with Gaussian
Hamiltonians $H_N^1(\vsi^1)$ and $H_N^2(\vsi^2)$ correspondingly, and these
configurations are coupled on the set where their overlap is fixed
$\{R_{1,2}=N^{-1}\sum_{i=1}^N \sigma_i^1\sigma_i^2 = u_N\}.$ We prove the
existence of the thermodynamic limit of the free energy of this system given
that $\lim_{N\to\infty}u_N = u\in[-1,1]$ and give the analogue of the
Aizenman-Sims-Starr variational principle that describes this limit via random
overlap structures.

15
The categories of this paper are: nucl-ex
34
The categories of this paper are: chem-ph
7
The categories of this paper are: hep-th
20
The categories of this paper are: acc-phys
12
The categories of this paper are: nucl-th
3
The categories of this paper are: physics
13
The categories of this paper are: quant-ph
27
The categories of this paper are: comp-gas
8
The categories of this paper are: hep-ex
36
The categories of this paper are: cmp-lg
17
The categories of this paper are: q-fin
33
The categories of this paper are: plasm-ph
14
The categories of this paper are: math-ph
10
The categories of this paper are: q-bio
19
The categories of this paper are: eess
35
The categories of this paper are: mtrl-th