Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Magnetism of Li doped La$_{2}$CuO$_4$: the antiferromagnetic
  spin-shard state   We study the dynamics of a single hole in Li and Sr doped La$_{2}$CuO$_4$ and
its extension to a finite hole concentration. We compare the physics of
La$_{2-x}$Sr$_x$CuO$_4$ and La$_{2}$Cu$_{1-x}$Li$_x$O$_4$ and explain why these
systems are remarkably different. We demonstrate that holes in
La$_{2}$Cu$_{1-x}$Li$_x$O$_4$ are always localized and that there is a critical
concentration, $x_c\approx 0.03$, above which the holes break the global
antiferromagnetic state into an array of weakly coupled antiferromagnetic
clusters (antiferromagnetic shards). We show that the spin-shard state provides
a description of the magnetic and electric properties of
La$_{2}$Cu$_{1-x}$Li$_x$O$_4$. Two experiments that can test our theory are
proposed.

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The categories of this paper are: physics
32
The categories of this paper are: atom-ph
10
The categories of this paper are: q-bio
8
The categories of this paper are: hep-ex
27
The categories of this paper are: comp-gas
15
The categories of this paper are: nucl-ex
35
The categories of this paper are: mtrl-th
28
The categories of this paper are: alg-geom
6
The categories of this paper are: astro-ph
13
The categories of this paper are: quant-ph
34
The categories of this paper are: chem-ph
24
The categories of this paper are: dg-ga
1
The categories of this paper are: cs
31
The categories of this paper are: ao-sci
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The categories of this paper are: stat
0
The categories of this paper are: hep-ph