Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Large-$n$ approach to thermodynamic Casimir effects in slabs with free
  surfaces   The classical $n$-vector $\phi^4$ model with $O(n)$ symmetrical Hamiltonian
${\cal H}$ is considered in a $\infty^2\times L$ slab geometry bounded by a
pair of parallel free surface planes at separation $L$. The
temperature-dependent scaling functions of the excess free energy and the
thermodynamic Casimir force are computed in the large-$n$ limit for
temperatures $T$ at, above, and below the bulk critical temperature $T_{\rm
c}$. Their $n=\infty$ limits can be expressed exactly in terms of the
eigensystem of a self-consistent one-dimensional Schr\"odinger equation. This
equation is solved by numerical means for two distinct discretized versions of
the model: in the first ("model A"), only the coordinate $z$ across the slab is
discretized and the integrations over momenta conjugate to the lateral
coordinates are regularized dimensionally; in the second ("model B"), a simple
cubic lattice with periodic boundary conditions along the lateral directions is
used. Renormalization-group ideas are invoked to show that, in addition to
corrections to scaling $\propto L^{-1}$, anomalous ones $\propto L^{-1}\ln L$
should occur. They can be considerably decreased by taking an appropriate
$g\to\infty$ ($T_{\rm c}\to\infty$) limit of the $\phi^4$ interaction constant
$g$. Depending on the model A or B, they can be absorbed completely or to a
large extent in an effective thickness $L_{\rm eff}=L+\delta L$. Excellent data
collapses and consistent high-precision results for both models are obtained.
The approach to the low-temperature Goldstone values of the scaling functions
is shown to involve logarithmic anomalies. The scaling functions exhibit all
qualitative features seen in experiments on the thinning of wetting layers of
${}^4$He and Monte Carlo simulations of $XY$ models, including a pronounced
minimum of the Casimir force below $T_{\rm c}$.

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The categories of this paper are: funct-an
17
The categories of this paper are: q-fin
26
The categories of this paper are: bayes-an
9
The categories of this paper are: nlin
0
The categories of this paper are: hep-ph
11
The categories of this paper are: hep-lat
3
The categories of this paper are: physics
14
The categories of this paper are: math-ph
25
The categories of this paper are: patt-sol
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The categories of this paper are: mtrl-th
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The categories of this paper are: solv-int
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The categories of this paper are: q-alg
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The categories of this paper are: quant-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: supr-con
12
The categories of this paper are: nucl-th