Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Structural phase transitions in Pr$_{1-x}$La$_{x}$AlO$_{3}$: Heat
  capacity and x-ray scattering studies   Structural phase transitions in Pr$_{1-x}$La$_x$AlO$_3$ (0 $\leq x\leq$ 1)
single crystals have been studied through heat capacity and high-resolution
x-ray scattering measurements. For PrAlO$_3$, the heat capacity shows a sharp
first-order peak at the rhombohedral to orthorhombic transition, while a
classical mean-field anomaly is observed at the orthorhombic to monoclinic
transition at lower temperatures. The transition temperature and the heat
capacity anomaly of the two transitions diminish with increasing $x$, and only
a single rhombohedral to monoclinic transition is observed for $x = 0.8$.
Although this latter transition is required by group theory to be first order,
no such evidence is found in the heat capacity and x-ray scattering
measurements. Instead, the results are consistent with mean-field criticality,
with a small distribution of transition temperature originating from weak
disorder.

30
The categories of this paper are: q-alg
9
The categories of this paper are: nlin
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The categories of this paper are: bayes-an
20
The categories of this paper are: acc-phys
17
The categories of this paper are: q-fin
5
The categories of this paper are: gr-qc
33
The categories of this paper are: plasm-ph
14
The categories of this paper are: math-ph
31
The categories of this paper are: ao-sci
16
The categories of this paper are: stat
24
The categories of this paper are: dg-ga
21
The categories of this paper are: adap-org
3
The categories of this paper are: physics
23
The categories of this paper are: solv-int
12
The categories of this paper are: nucl-th
1
The categories of this paper are: cs