Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Random Fuse Network as a Dipolar Magnet   We introduce an approximate mapping between the random fuse network (RFN) and
a random field dipolar Ising model (RFDIM). The state of the network damage is
associated with a metastable spin configuration. A mean-field treatment,
numerical solutions, and heuristic arguments support the broad validity of the
approximation and yield a generic phase diagram. At low disorder, the growth of
a single unstable `crack' leads to an abrupt global failure. Beyond a critical
disorder, the conducting network sustains significant damage before the
coalescence of cracks results in global failure.

18
The categories of this paper are: econ
13
The categories of this paper are: quant-ph
25
The categories of this paper are: patt-sol
0
The categories of this paper are: hep-ph
30
The categories of this paper are: q-alg
17
The categories of this paper are: q-fin
21
The categories of this paper are: adap-org
36
The categories of this paper are: cmp-lg
12
The categories of this paper are: nucl-th
28
The categories of this paper are: alg-geom
20
The categories of this paper are: acc-phys
5
The categories of this paper are: gr-qc
11
The categories of this paper are: hep-lat
7
The categories of this paper are: hep-th
35
The categories of this paper are: mtrl-th
27
The categories of this paper are: comp-gas