Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Asymptotic behaviour of ground states for mixtures of ferromagnetic and
  antiferromagnetic interactions in a dilute regime   We consider randomly distributed mixtures of bonds of ferromagnetic and
antiferromagnetic type in a two-dimensional square lattice with probability
$1-p$ and $p$, respectively, according to an i.i.d. random variable. We study
minimizers of the corresponding nearest-neighbour spin energy on large domains
in ${\mathbb Z}^2$. We prove that there exists $p_0$ such that for $p\le p_0$
such minimizers are characterized by a majority phase; i.e., they take
identically the value $1$ or $-1$ except for small disconnected sets. A
deterministic analogue is also proved.

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The categories of this paper are: astro-ph
18
The categories of this paper are: econ
21
The categories of this paper are: adap-org
17
The categories of this paper are: q-fin
12
The categories of this paper are: nucl-th
7
The categories of this paper are: hep-th
33
The categories of this paper are: plasm-ph
37
The categories of this paper are: supr-con
32
The categories of this paper are: atom-ph
20
The categories of this paper are: acc-phys
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The categories of this paper are: nucl-ex
13
The categories of this paper are: quant-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-ph
31
The categories of this paper are: ao-sci
36
The categories of this paper are: cmp-lg