Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Ginzburg-Landau theory of the zig-zag transition in
  quasi-one-dimensional classical Wigner crystals   We present a mean-field description of the zig-zag phase transition of a
quasi-one-dimensional system of strongly interacting particles, with
interaction potential $r^{-n}e^{-r/\lambda}$, that are confined by a power-law
potential ($y^{\alpha}$). The parameters of the resulting one-dimensional
Ginzburg-Landau theory are determined analytically for different values of
$\alpha$ and $n$. Close to the transition point for the zig-zag phase
transition, the scaling behavior of the order parameter is determined. For
$\alpha=2$ the zig-zag transition from a single to a double chain is of second
order, while for $\alpha>2$ the one chain configuration is always unstable and
for $\alpha<2$ the one chain ordered state becomes unstable at a certain
critical density resulting in jumps of single particles out of the chain.

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The categories of this paper are: hep-ph
13
The categories of this paper are: quant-ph
8
The categories of this paper are: hep-ex
7
The categories of this paper are: hep-th
11
The categories of this paper are: hep-lat
1
The categories of this paper are: cs
5
The categories of this paper are: gr-qc
15
The categories of this paper are: nucl-ex
10
The categories of this paper are: q-bio
14
The categories of this paper are: math-ph
16
The categories of this paper are: stat
32
The categories of this paper are: atom-ph
17
The categories of this paper are: q-fin
23
The categories of this paper are: solv-int
6
The categories of this paper are: astro-ph
31
The categories of this paper are: ao-sci