Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Effective field theory and the scattering process for magnons in the
  ferromagnet, antiferromagnet, and ferrimagnet   We discuss that a low-energy effective Lagrangian relying on SO(3)
$\rightarrow$ SO(2) is applicable for a ferrimagnet as well as a ferromagnet
and an antiferromagnet. The analysis of the particle states shows that there
exist not only massless modes with the dispersion relations $\omega \propto
|\bm{k}|,\, |\bm{k}|^2$, i.e., the so-called type-I and type-II Nambu-Goldstone
modes, respectively, but also gapped modes with $\omega \propto
m^2+|\bm{k}|^2$. We clarify how the coefficients of the terms with one time
derivative and those with two time derivatives in the effective Lagrangian
determine the order parameters specifying whether the system is in a
ferromagnetic, antiferromagnetic or ferrimagnetic state; we stress that the
gapped mode related to the spontaneous symmetry breaking appears only in the
ferrimagnetic system and not in the ferromagnetic and antiferromagnetic
systems. We also establish the power counting scheme and calculate the
scattering amplitudes and thereby the scattering lengths between the two
Nambu-Goldstone bosons. We show that the scattering length of the gapped mode
is finite and proportional to the gap. This characteristic property of the
gapped NG mode can be used to discriminate it from gapped excitations which
originate in other mechanisms. Finally, we study the effects of the explicit
symmetry breaking that are given by an external magnetic field and a single-ion
anisotropy, and show that the external magnetic fields do not have any effects
on the scattering amplitudes in all the spin systems as was known for the
ferromagnet system. In contrast, the anisotropy does affect the scattering
amplitudes, the phase shift, and the scattering length except for spin 1/2
systems. This result supports the possibility of the Efimov effect in spin
systems discussed in previous studies.

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The categories of this paper are: cmp-lg
15
The categories of this paper are: nucl-ex
5
The categories of this paper are: gr-qc
11
The categories of this paper are: hep-lat
9
The categories of this paper are: nlin
20
The categories of this paper are: acc-phys
37
The categories of this paper are: supr-con
10
The categories of this paper are: q-bio
23
The categories of this paper are: solv-int
33
The categories of this paper are: plasm-ph
26
The categories of this paper are: bayes-an
1
The categories of this paper are: cs
32
The categories of this paper are: atom-ph
14
The categories of this paper are: math-ph
34
The categories of this paper are: chem-ph
35
The categories of this paper are: mtrl-th