Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Exotic topological order in fractal spin liquids   We present a large class of three-dimensional spin models that possess
topological order with stability against local perturbations, but are beyond
description of topological quantum field theory. Conventional topological spin
liquids, on a formal level, may be viewed as condensation of string-like
extended objects with discrete gauge symmetries, being at fixed points with
continuous scale symmetries. In contrast, ground states of fractal spin liquids
are condensation of highly-fluctuating fractal objects with certain algebraic
symmetries, corresponding to limit cycles under real-space renormalization
group transformations which naturally arise from discrete scale symmetries of
underlying fractal geometries. A particular class of three-dimensional models
proposed in this paper may potentially saturate quantum information storage
capacity for local spin systems.

5
The categories of this paper are: gr-qc
35
The categories of this paper are: mtrl-th
33
The categories of this paper are: plasm-ph
24
The categories of this paper are: dg-ga
10
The categories of this paper are: q-bio
21
The categories of this paper are: adap-org
7
The categories of this paper are: hep-th
0
The categories of this paper are: hep-ph
23
The categories of this paper are: solv-int
6
The categories of this paper are: astro-ph
34
The categories of this paper are: chem-ph
1
The categories of this paper are: cs
31
The categories of this paper are: ao-sci
3
The categories of this paper are: physics
15
The categories of this paper are: nucl-ex
22
The categories of this paper are: chao-dyn