Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Magnetic three states of matter: A quantum Monte Carlo study of spin
  liquids   We present thermodynamic phase diagrams showing magnetic analog of "three
states of matter," namely, spin liquid, paramagnetic, and magnetically ordered
phases, obtained by unbiased quantum Monte Carlo simulations. Our simulations
are carried out for Kitaev's toric codes in two and three dimensions, i.e., the
simplest realizations of gapped topological $Z_2$ spin liquids, extended by a
nearest-neighbor ferromagnetic Ising coupling. We find that the ordered phase
borders on the spin liquid by a discontinuous transition line in three
dimensions, while it grows continuously from the quantum critical point in two
dimensions. In both cases, our results elucidate peculiar proximity effects to
the nearby spin liquids in the high-temperature paramagnetic phase, even when
the ground state is magnetically ordered. The thorough study of magnetic three
states of matter is achieved by introducing the "fictitious vertex" method into
the directed loop algorithm. This provides a generic prescription to simulate
models with off-diagonal multispin interactions, in which the conventional
scheme may suffer from intrinsic ergodicity breakdown as in the present case.

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The categories of this paper are: supr-con
17
The categories of this paper are: q-fin
28
The categories of this paper are: alg-geom
16
The categories of this paper are: stat
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The categories of this paper are: atom-ph
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The categories of this paper are: comp-gas
11
The categories of this paper are: hep-lat
24
The categories of this paper are: dg-ga
33
The categories of this paper are: plasm-ph
21
The categories of this paper are: adap-org
25
The categories of this paper are: patt-sol
15
The categories of this paper are: nucl-ex
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The categories of this paper are: mtrl-th
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The categories of this paper are: nlin
12
The categories of this paper are: nucl-th
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The categories of this paper are: cmp-lg