Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Nonequilibrium phase transition due to social group isolation   We introduce a simple model of a growing system with $m$ competing
communities. The model corresponds to the phenomenon of defeats suffered by
social groups living in isolation. A nonequilibrium phase transition is
observed when at critical time $t_c$ the first isolated cluster occurs. In the
one-dimensional system the volume of the new phase, i.e. the number of the
isolated individuals, increases with time as $Z \sim t^3$. For a large number
of possible communities the critical density of filled space equals to $\rho_c
= (m/N)^{1/3}$ where $N$ is the system size. A similar transition is observed
for Erd\H{o}s-R\'{e}nyi random graphs and Barab\'{a}si-Albert scale-free
networks. Analytic results are in agreement with numerical simulations.

18
The categories of this paper are: econ
28
The categories of this paper are: alg-geom
10
The categories of this paper are: q-bio
22
The categories of this paper are: chao-dyn
6
The categories of this paper are: astro-ph
17
The categories of this paper are: q-fin
25
The categories of this paper are: patt-sol
35
The categories of this paper are: mtrl-th
34
The categories of this paper are: chem-ph
31
The categories of this paper are: ao-sci
2
The categories of this paper are: math
7
The categories of this paper are: hep-th
16
The categories of this paper are: stat
33
The categories of this paper are: plasm-ph
24
The categories of this paper are: dg-ga
4
The categories of this paper are: cond-mat