Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An algorithmic proof for the completeness of two-dimensional Ising model   We show that the two dimensional Ising model is complete, in the sense that
the partition function of any lattice model on any graph is equal to the
partition function of the 2D Ising model with complex coupling. The latter
model has all its spin-spin coupling equal to i\pi/4 and all the parameters of
the original model are contained in the local magnetic fields of the Ising
model. This result has already been derived by using techniques from quantum
information theory and by exploiting the universality of cluster states. Here
we do not use the quantum formalism and hence make the completeness result
accessible to a wide audience. Furthermore our method has the advantage of
being algorithmic in nature so that by following a set of simple graphical
transformations, one is able to transform any discrete lattice model to an
Ising model defined on a (polynomially) larger 2D lattice.

27
The categories of this paper are: comp-gas
33
The categories of this paper are: plasm-ph
28
The categories of this paper are: alg-geom
20
The categories of this paper are: acc-phys
34
The categories of this paper are: chem-ph
32
The categories of this paper are: atom-ph
35
The categories of this paper are: mtrl-th
22
The categories of this paper are: chao-dyn
6
The categories of this paper are: astro-ph
31
The categories of this paper are: ao-sci
16
The categories of this paper are: stat
2
The categories of this paper are: math
36
The categories of this paper are: cmp-lg
29
The categories of this paper are: funct-an
17
The categories of this paper are: q-fin
9
The categories of this paper are: nlin