Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Two-Loop Crossover Scaling Functions of the O(N) Model   Using Environmentally Friendly Renormalization, we present an analytic
calculation of the series for the renormalization constants that describe the
equation of state for the $O(N)$ model in the whole critical region. The
solution of the beta-function equation, for the running coupling to order two
loops, exhibits crossover between the strong coupling fixed point, associated
with the Goldstone modes, and the Wilson-Fisher fixed point. The Wilson
functions $\gamma_\lambda$, $\gamma_\phi$ and $\gamma_{\phi^2}$, and thus the
effective critical exponents associated with renormalization of the transverse
vertex functions, also exhibit non-trivial crossover between these fixed
points.

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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: solv-int
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The categories of this paper are: q-fin
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The categories of this paper are: nucl-ex
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The categories of this paper are: adap-org
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The categories of this paper are: nlin
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The categories of this paper are: q-bio
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The categories of this paper are: math
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The categories of this paper are: nucl-th
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The categories of this paper are: patt-sol
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The categories of this paper are: physics
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The categories of this paper are: chem-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: plasm-ph
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The categories of this paper are: mtrl-th