Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The random cluster model and new summation and integration identities   We explicitly evaluate the free energy of the random cluster model at its
critical point for 0 < q < 4 using an exact result due to Baxter, Temperley and
Ashley. It is found that the resulting expression assumes a form which depends
on whether $\pi/2\cos^{-1}[\sqrt(q)/2]$ is a rational number, and if it is a
rational number whether the denominator is an odd integer. Our consideration
leads to new summation identities and, for q = 2, a closed-form evaluation of
the integral [1/(4\pi^2)] \int_0^{2\pi}dx \int_0^{2\pi}dy ln[A + B + C - A cos
x - B cos y - C cos(x + y)] = -\ln(2S) + (2/\pi)[Ti_2(AS) + Ti_2(BS) +
Ti_2(CS)], where A, B, C >=0 and S = 1/\sqrt{AB+BC+CA}.

22
The categories of this paper are: chao-dyn
17
The categories of this paper are: q-fin
20
The categories of this paper are: acc-phys
32
The categories of this paper are: atom-ph
7
The categories of this paper are: hep-th
16
The categories of this paper are: stat
26
The categories of this paper are: bayes-an
36
The categories of this paper are: cmp-lg
21
The categories of this paper are: adap-org
27
The categories of this paper are: comp-gas
11
The categories of this paper are: hep-lat
5
The categories of this paper are: gr-qc
0
The categories of this paper are: hep-ph
15
The categories of this paper are: nucl-ex
28
The categories of this paper are: alg-geom
9
The categories of this paper are: nlin