Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Atomistic treatment of depolarizing energy and field in ferroelectric
  nanostructures   An {\it atomistic} approach allowing an accurate and efficient treatment of
depolarizing energy and field in {\it any} low-dimensional ferroelectric
structure is developed. Application of this approach demonstrates the limits of
the widely used continuum model (even) for simple test cases. Moreover,
implementation of this approach within a first-principles-based model reveals
an unusual phase transition -- from a state exhibiting a spontaneous
polarization to a phase associated with a toroid moment of polarization -- in a
ferroelectric nanodot for a critical value of the depolarizing field.

35
The categories of this paper are: mtrl-th
12
The categories of this paper are: nucl-th
2
The categories of this paper are: math
32
The categories of this paper are: atom-ph
33
The categories of this paper are: plasm-ph
8
The categories of this paper are: hep-ex
10
The categories of this paper are: q-bio
23
The categories of this paper are: solv-int
6
The categories of this paper are: astro-ph
9
The categories of this paper are: nlin
25
The categories of this paper are: patt-sol
22
The categories of this paper are: chao-dyn
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The categories of this paper are: bayes-an
20
The categories of this paper are: acc-phys
30
The categories of this paper are: q-alg
13
The categories of this paper are: quant-ph