Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: High-precision Monte Carlo study of several models in the
  three-dimensional U(1) universality class   We present a worm-type Monte Carlo study of several typical models in the
three-dimensional (3D) U(1) universality class, which include the classical 3D
XY model in the directed flow representation and its Villain version, as well
as the 2D quantum Bose-Hubbard (BH) model with unitary filling in the
imaginary-time world-line representation. From the topology of the
configurations on a torus, we sample the superfluid stiffness $\rho_s$ and the
dimensionless wrapping probability $R$. From the finite-size scaling analyses
of $\rho_s$ and of $R$, we determine the critical points as $T_c ({\rm XY})
=2.201\, 844 \,1(5)$ and $T_c ({\rm Villain})=0.333\, 067\, 04(7)$ and $(t/U)_c
({\rm BH})=0.059 \, 729 \,1(8)$, where $T$ is the temperature for the classical
models, and $t$ and $U$ are respectively the hopping and on-site interaction
strength for the BH model. The precision of our estimates improves
significantly over that of the existing results. Moreover, it is observed that
at criticality, the derivative of a wrapping probability with respect to $T$
suffers from negligible leading corrections and enables a precise determination
of the correlation length critical exponent as $\nu=0.671 \, 83(18)$. In
addition, the critical exponent $\eta$ is estimated as $\eta=0.038 \, 53(48)$
by analyzing a susceptibility-like quantity. We believe that these numerical
results would provide a solid reference in the study of classical and quantum
phase transitions in the 3D U(1) universality, including the recent development
of the conformal bootstrap method.

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The categories of this paper are: adap-org
32
The categories of this paper are: atom-ph
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The categories of this paper are: stat
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The categories of this paper are: plasm-ph
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The categories of this paper are: supr-con
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The categories of this paper are: cmp-lg
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The categories of this paper are: cs
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The categories of this paper are: q-alg
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: astro-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: nucl-ex
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The categories of this paper are: physics
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The categories of this paper are: math-ph