Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Effects of two-loop contributions in the pseudofermion functional
  renormalization group method for quantum spin systems   We implement an extension of the pseudofermion functional renormalization
group (PFFRG) method for quantum spin systems that takes into account two-loop
diagrammatic contributions. An efficient numerical treatment of the additional
terms is achieved within a nested graph construction which recombines different
one-loop interaction channels. In order to be fully self consistent with
respect to self-energy corrections we also include certain three-loop terms of
Katanin type. We first apply this formalism to the antiferromagnetic
$J_1$-$J_2$ Heisenberg model on the square lattice and benchmark our results
against the previous one-loop plus Katanin approach. Even though the RG
equations undergo significant modifications when including the two-loop terms,
the magnetic phase diagram -- comprising N\'eel ordered and collinear ordered
phases separated by a magnetically disordered regime -- remains remarkably
unchanged. Only the boundary position between the disordered and the collinear
phases is found to be moderately affected by two-loop terms. On the other hand,
critical RG scales, which we associate with critical temperatures $T_\text{c}$,
are reduced by a factor of $\sim2$ indicating that the two-loop diagrams play a
significant role in enforcing the Mermin-Wagner theorem. Improved estimates for
critical temperatures are also obtained for the Heisenberg ferromagnet on the
3D simple cubic lattice where errors in $T_\text{c}$ are reduced by $\sim34\%$.

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The categories of this paper are: q-bio
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The categories of this paper are: chao-dyn
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The categories of this paper are: adap-org
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The categories of this paper are: cmp-lg
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The categories of this paper are: physics
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The categories of this paper are: astro-ph
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The categories of this paper are: stat
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The categories of this paper are: hep-th
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The categories of this paper are: ao-sci
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The categories of this paper are: chem-ph
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The categories of this paper are: solv-int
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The categories of this paper are: gr-qc
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The categories of this paper are: econ
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The categories of this paper are: q-alg
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The categories of this paper are: cs
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The categories of this paper are: math