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The random cluster model and new summation and integration identities | | L. C. Chen
; F. Y. Wu
; | | Date: |
11 Dec 2004 | | Subject: | Statistical Mechanics | cond-mat.stat-mech | | Abstract: | 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 $pi/2cos^{-1}[sqrt(q)/2]$ 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/(4pi^2)] int_0^{2pi}dx int_0^{2pi}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}. | | Source: | arXiv, cond-mat/0501228 | | Services: | Forum | Review | PDF | Favorites | |
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