Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The critical Casimir force and its fluctuations in lattice spin models:
  exact and Monte Carlo results   We present general arguments and construct a stress tensor operator for
finite lattice spin models. The average value of this operator gives the
Casimir force of the system close to the bulk critical temperature $T_c$. We
verify our arguments via exact results for the force in the two-dimensional
Ising model, $d$-dimensional Gaussian and mean spherical model with $2<d<4$. On
the basis of these exact results and by Monte Carlo simulations for
three-dimensional Ising, XY and Heisenberg models we demonstrate that the
standard deviation of the Casimir force $F_C$ in a slab geometry confining a
critical substance in-between is $k_b T D(T)(A/a^{d-1})^{1/2}$, where $A$ is
the surface area of the plates, $a$ is the lattice spacing and $D(T)$ is a
slowly varying nonuniversal function of the temperature $T$. The numerical
calculations demonstrate that at the critical temperature $T_c$ the force
possesses a Gaussian distribution centered at the mean value of the force
$<F_C>=k_b T_c (d-1)\Delta/(L/a)^{d}$, where $L$ is the distance between the
plates and $\Delta$ is the (universal) Casimir amplitude.

11
The categories of this paper are: hep-lat
1
The categories of this paper are: cs
24
The categories of this paper are: dg-ga
20
The categories of this paper are: acc-phys
3
The categories of this paper are: physics
25
The categories of this paper are: patt-sol
29
The categories of this paper are: funct-an
31
The categories of this paper are: ao-sci
23
The categories of this paper are: solv-int
0
The categories of this paper are: hep-ph
37
The categories of this paper are: supr-con
33
The categories of this paper are: plasm-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: q-fin
34
The categories of this paper are: chem-ph
21
The categories of this paper are: adap-org