Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A model with symmetry-breaking phase transition triggered by a
  double-well potential   In some recent papers some theorems on sufficiency conditions for the
occurrence of a $\mathbb{Z}_2$-symmetry breaking phase transition
($\mathbb{Z}_2$-SBPT) have been showed making use of geometric-topological
concepts of potential energy landscapes. In particular, a $\mathbb{Z}_2$-SBPT
can be triggered by double-well potentials, or in an equivalent way, by
dumbbell-shaped equipotential surfaces. In this paper we introduce a model with
a classical $\mathbb{Z}_2$-SBPT which, due to its essential feature, shows in
the clearest way the generating-mechanism of a $\mathbb{Z}_2$-SBPT above
mentioned. Despite the model is not a physical model, it has all the features
of such a model with the same kind of SBPT. At the end of the paper a
comparison with the $\phi^4$ model is made. The model may be useful for
didactic purposes.

11
The categories of this paper are: hep-lat
13
The categories of this paper are: quant-ph
21
The categories of this paper are: adap-org
31
The categories of this paper are: ao-sci
30
The categories of this paper are: q-alg
34
The categories of this paper are: chem-ph
14
The categories of this paper are: math-ph
33
The categories of this paper are: plasm-ph
36
The categories of this paper are: cmp-lg
22
The categories of this paper are: chao-dyn
1
The categories of this paper are: cs
0
The categories of this paper are: hep-ph
6
The categories of this paper are: astro-ph
5
The categories of this paper are: gr-qc
16
The categories of this paper are: stat
9
The categories of this paper are: nlin