Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Minimal renormalization without epsilon-expansion: Amplitude functions
  in three dimensions below T_c   Massive field theory at fixed dimension d<4 is combined with the minimal
subtraction scheme to calculate the amplitude functions of thermodynamic
quantities for the O(n) symmetric phi^4 model below T_c in two-loop order.
Goldstone singularities arising at an intermediate stage in the calculation of
O(n) symmetric quantities are shown to cancel among themselves leaving a finite
result in the limit of zero external field. From the free energy we calculate
the amplitude functions in zero field for the order parameter, specific heat
and helicity modulus (superfluid density) in three dimensions. We also
calculate the q^2 part of the inverse of the wavenumber-dependent transverse
susceptibility chi_T(q) which provides an independent check of our result for
the helicity modulus. The two-loop contributions to the superfluid density and
specific heat below T_c turn out to be comparable in magnitude to the one-loop
contributions, indicating the necessity of higher-order calculations and
Pade-Borel type resummations.

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The categories of this paper are: q-alg
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The categories of this paper are: alg-geom
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The categories of this paper are: acc-phys
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The categories of this paper are: gr-qc
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: mtrl-th
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The categories of this paper are: eess
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The categories of this paper are: q-fin
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The categories of this paper are: math-ph
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The categories of this paper are: physics
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The categories of this paper are: adap-org
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The categories of this paper are: solv-int
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The categories of this paper are: hep-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: ao-sci