Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Multiple critical behavior of probabilistic limit theorems in the
  neighborhood of a tricritical point   We derive probabilistic limit theorems that reveal the intricate structure of
the phase transitions in a mean-field version of the Blume-Emery-Griffiths
model. These probabilistic limit theorems consist of scaling limits for the
total spin and moderate deviation principles (MDPs) for the total spin. The
model under study is defined by a probability distribution that depends on the
parameters $n$, $\beta$, and $K$, which represent, respectively, the number of
spins, the inverse temperature, and the interaction strength. The intricate
structure of the phase transitions is revealed by the existence of 18 scaling
limits and 18 MDPs for the total spin. These limit results are obtained as
$(\beta,K)$ converges along appropriate sequences to points belonging to
various subsets of the phase diagram, which include a curve of second-order
points and a tricritical point. The forms of the limiting densities in the
scaling limits and of the rate functions in the MDPs reflect the influence of
one or more sets that lie in neighborhoods of the critical points and the
tricritical point. Of all the scaling limits, the structure of those near the
tricritical point is by far the most complex, exhibiting new types of critical
behavior when observed in a limit-theorem phase diagram in the space of the two
parameters that parametrize the scaling limits.

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The categories of this paper are: hep-ph
25
The categories of this paper are: patt-sol
27
The categories of this paper are: comp-gas
37
The categories of this paper are: supr-con
35
The categories of this paper are: mtrl-th
21
The categories of this paper are: adap-org
17
The categories of this paper are: q-fin
1
The categories of this paper are: cs
20
The categories of this paper are: acc-phys
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The categories of this paper are: math
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The categories of this paper are: econ
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The categories of this paper are: alg-geom
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The categories of this paper are: dg-ga
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-ex
33
The categories of this paper are: plasm-ph