Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Topological Defects on the Lattice I: The Ising model   In this paper and its sequel, we construct topologically invariant defects in
two-dimensional classical lattice models and quantum spin chains. We show how
defect lines commute with the transfer matrix/Hamiltonian when they obey the
defect commutation relations, cousins of the Yang-Baxter equation. These
relations and their solutions can be extended to allow defect lines to branch
and fuse, again with properties depending only on topology. In this part I, we
focus on the simplest example, the Ising model. We define lattice spin-flip and
duality defects and their branching, and prove they are topological. One useful
consequence is a simple implementation of Kramers-Wannier duality on the torus
and higher genus surfaces by using the fusion of duality defects. We use these
topological defects to do simple calculations that yield exact properties of
the conformal field theory describing the continuum limit. For example, the
shift in momentum quantization with duality-twisted boundary conditions yields
the conformal spin 1/16 of the chiral spin field. Even more strikingly, we
derive the modular transformation matrices explicitly and exactly.

32
The categories of this paper are: atom-ph
17
The categories of this paper are: q-fin
10
The categories of this paper are: q-bio
11
The categories of this paper are: hep-lat
33
The categories of this paper are: plasm-ph
3
The categories of this paper are: physics
36
The categories of this paper are: cmp-lg
30
The categories of this paper are: q-alg
15
The categories of this paper are: nucl-ex
25
The categories of this paper are: patt-sol
9
The categories of this paper are: nlin
23
The categories of this paper are: solv-int
37
The categories of this paper are: supr-con
8
The categories of this paper are: hep-ex
35
The categories of this paper are: mtrl-th
22
The categories of this paper are: chao-dyn