Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Phase transitions in the two-dimensional single-ion anisotropic
  ferromagnetic with long-range interactions   In the present work, we investigate the effects of long-range interactions on
the phase transitions of two-dimensional ferromagnetic models with single-ion
anisotropy at zero and finite temperatures. The Hamiltonian is given by
$H=\sum_{i\neq j} J_{ij}(S_i^xS_j^x+S_i^yS_j^y+\lambda
S_i^zS_j^z)+D\sum_{i}(S_i^z)^2$, where $J_{ij}=-J |r_j-r_i|^{-p}$ ($p\geq 3$)
is a long-range ferromagnetic interaction ($J>0$), $0\leq \lambda\leq 1$ is an
anisotropic constant and $D$ is the single-ion anisotropic constant. It is
well-known that the single-ion anisotropy $D$ creates a competition between an
ordered state (favored by the exchange interaction) and a disordered state,
even at zero temperature. For small values of $D$, the system has a spontaneous
magnetization $m_z\neq 0$, while in the large-D phase $m_z=0$ because a state
with $\langle S^z\rangle\neq 0$ is energetically unfavorable. Therefore, a
phase transition due to quantum fluctuations occurs in some critical value
$D_c$. For systems with short-range interaction $D_c\approx 6J$, depending of
$\lambda$ constant, but in our model we have found larger values of $D$ due to
the higher cost to flip a spin. Since low-dimensional magnetic systems with
long range interaction can be ordered at finite temperature, we also have
analyzed the thermal phase transitions (similar to the BKT transition). The
model has been studied by using a Schwinger boson formalism as well as the
Self-consistent Harmonic Approximation (SCHA) and both methods provide
according results.

6
The categories of this paper are: astro-ph
0
The categories of this paper are: hep-ph
10
The categories of this paper are: q-bio
17
The categories of this paper are: q-fin
27
The categories of this paper are: comp-gas
2
The categories of this paper are: math
5
The categories of this paper are: gr-qc
15
The categories of this paper are: nucl-ex
31
The categories of this paper are: ao-sci
26
The categories of this paper are: bayes-an
28
The categories of this paper are: alg-geom
22
The categories of this paper are: chao-dyn
19
The categories of this paper are: eess
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The categories of this paper are: physics
1
The categories of this paper are: cs
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The categories of this paper are: quant-ph