Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Some Exact Results on the Potts Model Partition Function in a Magnetic
  Field   We consider the Potts model in a magnetic field on an arbitrary graph $G$.
Using a formula of F. Y. Wu for the partition function $Z$ of this model as a
sum over spanning subgraphs of $G$, we prove some properties of $Z$ concerning
factorization, monotonicity, and zeros. A generalization of the Tutte
polynomial is presented that corresponds to this partition function. In this
context we formulate and discuss two weighted graph-coloring problems. We also
give a general structural result for $Z$ for cyclic strip graphs.

27
The categories of this paper are: comp-gas
31
The categories of this paper are: ao-sci
21
The categories of this paper are: adap-org
28
The categories of this paper are: alg-geom
14
The categories of this paper are: math-ph
20
The categories of this paper are: acc-phys
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The categories of this paper are: dg-ga
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The categories of this paper are: eess
10
The categories of this paper are: q-bio
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The categories of this paper are: q-alg
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The categories of this paper are: funct-an
7
The categories of this paper are: hep-th
5
The categories of this paper are: gr-qc
8
The categories of this paper are: hep-ex
35
The categories of this paper are: mtrl-th
25
The categories of this paper are: patt-sol