Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The O(n) $\phi^4$ model with free surfaces in the large-$n$ limit: Some
  exact results for boundary critical behaviour, fluctuation-induced forces and
  distant-wall corrections   The $O(n)$ ${\phi}^4$ model on a slab $\mathbb{R}^{d-1}\times[0,L]$ bounded
by free surfaces is studied for $2<d<4$ in the limit $n\to\infty$. The
self-consistent potential $V(z)$ which the exact $n\to\infty$ solution of the
model involves is analysed by means of boundary operator expansions. Building
on the known exact $n\to\infty$ solution for $V(z)$ in the semi-infinite case
$L=\infty$ at the bulk critical point, we exactly determine two types of
corrections to this potential: (i) those linear in the temperature scaling
field $t$ at $L=\infty$, and (ii) the leading $L$-dependent (distant-wall)
corrections at the critical point. From (i) exact analytical results at $d=3$
are obtained for the leading temperature singularity of the excess surface free
energy and the implied asymptotic behaviours of the scaling functions
$\Theta_3(x)$ and $\vartheta_3(x)$ of the residual free energy $f_{\rm res}
=L^{1-d}\,\Theta_d(tL)$ and the critical Casimir force $\beta\mathcal{F}_{\rm
C}(T,L)=L^{-d}\,\vartheta_d(tL)$ in the limit $x\to 0\pm$. The second
derivative $\vartheta_3''(0)$ is computed exactly.

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The categories of this paper are: hep-ph
20
The categories of this paper are: acc-phys
9
The categories of this paper are: nlin
28
The categories of this paper are: alg-geom
36
The categories of this paper are: cmp-lg
37
The categories of this paper are: supr-con
34
The categories of this paper are: chem-ph
8
The categories of this paper are: hep-ex
19
The categories of this paper are: eess
1
The categories of this paper are: cs
5
The categories of this paper are: gr-qc
32
The categories of this paper are: atom-ph
18
The categories of this paper are: econ
31
The categories of this paper are: ao-sci
16
The categories of this paper are: stat
2
The categories of this paper are: math