Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: String and Membrane condensation on 3D lattices   In this paper, we investigate the general properties of lattice spin models
that have string and/or membrane condensed ground states. We discuss the
properties needed to define a string or membrane operator. We study three 3D
spin models which lead to Z_2 gauge theory at low energies. All the three
models are exactly soluble and produce topologically ordered ground states. The
first model contains both closed-string and closed-membrane condensations. The
second model contains closed-string condensation only. The ends of open-strings
behave like fermionic particles. The third model also has condensations of
closed membranes and closed strings. The ends of open strings are bosonic while
the edges of open membranes are fermionic. The third model contains a new type
of topological order.

34
The categories of this paper are: chem-ph
37
The categories of this paper are: supr-con
30
The categories of this paper are: q-alg
0
The categories of this paper are: hep-ph
17
The categories of this paper are: q-fin
33
The categories of this paper are: plasm-ph
15
The categories of this paper are: nucl-ex
2
The categories of this paper are: math
31
The categories of this paper are: ao-sci
32
The categories of this paper are: atom-ph
14
The categories of this paper are: math-ph
36
The categories of this paper are: cmp-lg
6
The categories of this paper are: astro-ph
23
The categories of this paper are: solv-int
3
The categories of this paper are: physics
11
The categories of this paper are: hep-lat