Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The degree distribution in bipartite planar maps: applications to the
  Ising model   We characterize the generating function of bipartite planar maps counted
according to the degree distribution of their black and white vertices. This
result is applied to the solution of the hard particle and Ising models on
random planar lattices. We thus recover and extend some results previously
obtained by means of matrix integrals.
  Proofs are purely combinatorial and rely on the idea that planar maps are
conjugacy classes of trees. In particular, these trees explain why the
solutions of the Ising and hard particle models on maps of bounded degree are
always algebraic.

16
The categories of this paper are: stat
21
The categories of this paper are: adap-org
4
The categories of this paper are: cond-mat
20
The categories of this paper are: acc-phys
23
The categories of this paper are: solv-int
34
The categories of this paper are: chem-ph
27
The categories of this paper are: comp-gas
31
The categories of this paper are: ao-sci
26
The categories of this paper are: bayes-an
35
The categories of this paper are: mtrl-th
8
The categories of this paper are: hep-ex
13
The categories of this paper are: quant-ph
24
The categories of this paper are: dg-ga
3
The categories of this paper are: physics
18
The categories of this paper are: econ
30
The categories of this paper are: q-alg