Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Magnetic quantum phase transitions of the antiferromagnetic J_{1}-J_{2}
  Heisenberg model   We obtain the complete phase diagram of the antiferromagnetic $J_{1}$-$J_{2}$
model, $0\leq \alpha = J_2/J1 \leq 1$, within the framework of the $O(N)$
nonlinear sigma model. We find two magnetically ordered phases, one with N\'
eel order, for $\alpha \leq 0.4$, and another with collinear order, for
$\alpha\geq 0.6$, separated by a nonmagnetic region, for $0.4\leq \alpha \leq
0.6$, where a gapped spin liquid is found. The transition at $\alpha=0.4$ is of
the second order while the one at $\alpha=0.6$ is of the first order and the
spin gaps cross at $\alpha=0.5$. Our results are exact at $N\rightarrow\infty$
and agree with numerical results from different methods.

23
The categories of this paper are: solv-int
14
The categories of this paper are: math-ph
9
The categories of this paper are: nlin
36
The categories of this paper are: cmp-lg
26
The categories of this paper are: bayes-an
30
The categories of this paper are: q-alg
10
The categories of this paper are: q-bio
5
The categories of this paper are: gr-qc
16
The categories of this paper are: stat
27
The categories of this paper are: comp-gas
35
The categories of this paper are: mtrl-th
21
The categories of this paper are: adap-org
28
The categories of this paper are: alg-geom
32
The categories of this paper are: atom-ph
37
The categories of this paper are: supr-con
29
The categories of this paper are: funct-an