Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Topological conditions for discrete symmetry breaking and phase
  transitions   In the framework of a recently proposed topological approach to phase
transitions, some sufficient conditions ensuring the presence of the
spontaneous breaking of a Z_2 symmetry and of a symmetry-breaking phase
transition are introduced and discussed. A very simple model, which we refer to
as the hypercubic model, is introduced and solved. The main purpose of this
model is that of illustrating the content of the sufficient conditions, but it
is interesting also in itself due to its simplicity. Then some mean-field
models already known in the literature are discussed in the light of the
sufficient conditions introduced here.

15
The categories of this paper are: nucl-ex
14
The categories of this paper are: math-ph
18
The categories of this paper are: econ
23
The categories of this paper are: solv-int
32
The categories of this paper are: atom-ph
35
The categories of this paper are: mtrl-th
2
The categories of this paper are: math
31
The categories of this paper are: ao-sci
7
The categories of this paper are: hep-th
22
The categories of this paper are: chao-dyn
21
The categories of this paper are: adap-org
37
The categories of this paper are: supr-con
28
The categories of this paper are: alg-geom
20
The categories of this paper are: acc-phys
27
The categories of this paper are: comp-gas
3
The categories of this paper are: physics