  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}.
