Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Fracture and second-order phase transitions   Using the global fiber bundle model as a tractable scheme of progressive
fracture in heterogeneous materials, we define the branching ratio in
avalanches as a suitable order parameter to clarify the order of the phase
transition occurring at the collapse of the system. The model is analyzed using
a probabilistic approach suited to smooth fluctuations. The branching ratio
shows a behavior analogous to the magnetization in known magnetic systems with
2nd-order phase transitions. We obtain a universal critical exponent
$\beta\approx 0.5$ independent of the probability distribution used to assign
the strengths of individual fibers.

31
The categories of this paper are: ao-sci
5
The categories of this paper are: gr-qc
1
The categories of this paper are: cs
34
The categories of this paper are: chem-ph
0
The categories of this paper are: hep-ph
32
The categories of this paper are: atom-ph
35
The categories of this paper are: mtrl-th
9
The categories of this paper are: nlin
33
The categories of this paper are: plasm-ph
3
The categories of this paper are: physics
19
The categories of this paper are: eess
2
The categories of this paper are: math
17
The categories of this paper are: q-fin
21
The categories of this paper are: adap-org
23
The categories of this paper are: solv-int
22
The categories of this paper are: chao-dyn