Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Multifractality in random networks with power-law decaying bond
  strengths   In this paper we demonstrate numerically that random networks whose adjacency
matrices ${\bf A}$ are represented by a diluted version of the Power--Law
Banded Random Matrix (PBRM) model have multifractal eigenfunctions. The PBRM
model describes one--dimensional samples with random long--range bonds. The
bond strengths of the model, which decay as a power--law, are tuned by the
parameter $\mu$ as $A_{mn}\propto |m-n|^{-\mu}$; while the sparsity is driven
by the average network connectivity $\alpha$: for $\alpha=0$ the vertices in
the network are isolated and for $\alpha=1$ the network is fully connected and
the PBRM model is recovered. Though it is known that the PBRM model has
multifractal eigenfunctions at the critical value $\mu=\mu_c=1$, we clearly
show [from the scaling of the relative fluctuation of the participation number
$I_2$ as well as the scaling of the probability distribution functions $P(\ln
I_2)$] the existence of the critical value $\mu_c\equiv \mu_c(\alpha)$ for
$\alpha<1$. Moreover, we characterise the multifractality of the eigenfunctions
of our random network model by the use of the corresponding multifractal
dimensions $D_q$, that we compute from the finite network-size scaling of the
typical eigenfunction participation numbers $\exp\left\langle\ln I_q
\right\rangle$.

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The categories of this paper are: hep-th
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The categories of this paper are: nlin
34
The categories of this paper are: chem-ph
26
The categories of this paper are: bayes-an
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The categories of this paper are: nucl-ex
32
The categories of this paper are: atom-ph
4
The categories of this paper are: cond-mat
10
The categories of this paper are: q-bio
0
The categories of this paper are: hep-ph
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The categories of this paper are: math-ph
36
The categories of this paper are: cmp-lg
31
The categories of this paper are: ao-sci
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The categories of this paper are: q-fin
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The categories of this paper are: quant-ph
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The categories of this paper are: supr-con
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The categories of this paper are: cs