Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Monte Carlo Study of a $U(1)\times U(1)$ Loop Model with Modular
  Invariance   We study a $U(1)\times U(1)$ system in (2+1)-dimensions with long-range
interactions and mutual statistics. The model has the same form after the
application of operations from the modular group, a property which we call
modular invariance. Using the modular invariance of the model, we propose a
possible phase diagram. We obtain a sign-free reformulation of the model and
study it in Monte Carlo. This study confirms our proposed phase diagram. We use
the modular invariance to analytically determine the current-current
correlation functions and conductivities in all the phases in the diagram, as
well as at special "fixed" points which are unchanged by an operation from the
modular group. We numerically determine the order of the phase transitions, and
find segments of second-order transitions. For the statistical interaction
parameter $\theta=\pi$, these second-order transitions are evidence of a
critical loop phase obtained when both loops are trying to condense
simulataneously. We also measure the critical exponents of the second-order
transitions.

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The categories of this paper are: patt-sol
30
The categories of this paper are: q-alg
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-th
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The categories of this paper are: quant-ph
3
The categories of this paper are: physics
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The categories of this paper are: eess
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The categories of this paper are: chem-ph
18
The categories of this paper are: econ
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The categories of this paper are: alg-geom
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The categories of this paper are: plasm-ph
0
The categories of this paper are: hep-ph
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The categories of this paper are: stat
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The categories of this paper are: nucl-ex
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-ex