Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Renormalization Group Approach to Percolation in Hierarchical Lattices   Percolation refers to an interesting class of problems related to the
properties of disordered systems, usually formulated in terms of objects
randomly placed on an underlying lattice or continuum. Despite the simplicity
of the setup, most percolative systems undergo a phase transition from a
disconnected state with many disjoint clusters to a state where a finite
fraction of the lattice sites are connected to a single cluster. As in the case
of thermodynamic phase transitions, power law dependencies generically near the
critical percolation threshold. The origin of these dependencies can be
understood through the lens of scaling and renormalization, and indeed many
quantitative results can be acquired using these tools. In this paper we study
the percolation problem on a hierarchical lattice, where exact results for the
critical exponents can be obtained from a decimation procedure. We calculate
analytic results for the full set of geometric critical exponents and confirm
their consistency with simulation. Finally, we set up an interesting
renormalization group for the conductivity of the system and use it to
computationally extract the conductivity exponent t.

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The categories of this paper are: atom-ph
10
The categories of this paper are: q-bio
20
The categories of this paper are: acc-phys
12
The categories of this paper are: nucl-th
24
The categories of this paper are: dg-ga
16
The categories of this paper are: stat
1
The categories of this paper are: cs
22
The categories of this paper are: chao-dyn
3
The categories of this paper are: physics
25
The categories of this paper are: patt-sol
7
The categories of this paper are: hep-th
18
The categories of this paper are: econ
34
The categories of this paper are: chem-ph
11
The categories of this paper are: hep-lat
23
The categories of this paper are: solv-int
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The categories of this paper are: alg-geom