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Title: The Ramdom Cluster Model and New Summation and Integration Identities
Authors: 陳隆奇
Chen, L. C.
Wu, F. Y.
Contributors: 應數系
Date: 2005-08
Issue Date: 2017-06-27 17:09:27 (UTC+8)
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 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}.
Relation: J.Phys. A:Math. Gen., Vol.38, pp.6271-6276
Data Type: article
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