Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Microscopic theory of phase transitions in a critical region   The problem of finding a microscopic theory of phase transitions across a
critical point is a central unsolved problem in theoretical physics. We find a
general solution to that problem and present it here for the cases of
Bose-Einstein condensation in an interacting gas and ferromagnetism in a
lattice of spins, interacting via a Heisenberg or Ising Hamiltonian. For
Bose-Einstein condensation, we present the exact, valid for the entire critical
region, equations for the Green functions and order parameter, that is a
critical-region extension of the Beliaev-Popov and Gross-Pitaevskii equations.
For the magnetic phase transition, we find an exact theory in terms of
constrained bosons in a lattice and obtain similar equations for the Green
functions and order parameter. In particular, we outline an exact solution for
the three-dimensional Ising model.

31
The categories of this paper are: ao-sci
2
The categories of this paper are: math
13
The categories of this paper are: quant-ph
29
The categories of this paper are: funct-an
23
The categories of this paper are: solv-int
1
The categories of this paper are: cs
32
The categories of this paper are: atom-ph
11
The categories of this paper are: hep-lat
37
The categories of this paper are: supr-con
16
The categories of this paper are: stat
33
The categories of this paper are: plasm-ph
21
The categories of this paper are: adap-org
6
The categories of this paper are: astro-ph
20
The categories of this paper are: acc-phys
28
The categories of this paper are: alg-geom
12
The categories of this paper are: nucl-th