Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Successive phase transitions and kink solutions in $\phi^{8}$,
  $\phi^{10}$, and $\phi^{12}$ field theories   We obtain exact solutions for kinks in $\phi^{8}$, $\phi^{10}$ and
$\phi^{12}$ field theories with degenerate minima, which can describe a
second-order phase transition followed by a first-order one, a succession of
two first-order phase transitions and a second-order phase transition followed
by two first-order phase transitions, respectively. Such phase transitions are
known to occur in ferroelastic and ferroelectric crystals and in meson physics.
In particular, we find that the higher-order field theories have kink solutions
with algebraically-decaying tails and also asymmetric cases with mixed
exponential-algebraic tail decay, unlike the lower-order $\phi^4$ and $\phi^6$
theories. Additionally, we construct distinct kinks with equal energies in all
three field theories considered, and we show the co-existence of up to three
distinct kinks (for a $\phi^{12}$ potential with six degenerate minima). We
also summarize phonon dispersion relations for these systems, showing that the
higher-order field theories have specific cases in which only nonlinear phonons
are allowed. For the $\phi^{10}$ field theory, which is a quasi-exactly
solvable (QES) model akin to $\phi^6$, we are also able to obtain three
analytical solutions for the classical free energy as well as the probability
distribution function in the thermodynamic limit.

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The categories of this paper are: hep-ex
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The categories of this paper are: comp-gas
30
The categories of this paper are: q-alg
0
The categories of this paper are: hep-ph
18
The categories of this paper are: econ
20
The categories of this paper are: acc-phys
36
The categories of this paper are: cmp-lg
37
The categories of this paper are: supr-con
6
The categories of this paper are: astro-ph
31
The categories of this paper are: ao-sci
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The categories of this paper are: stat
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The categories of this paper are: hep-lat
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The categories of this paper are: quant-ph
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The categories of this paper are: adap-org
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The categories of this paper are: eess
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The categories of this paper are: chao-dyn