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    政大機構典藏 > 理學院 > 應用數學系 > 期刊論文 >  Item 140.119/110508


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    題名: The Ramdom Cluster Model and New Summation and Integration Identities
    作者: 陳隆奇
    Chen, L. C.
    Wu, F. Y.
    貢獻者: 應數系
    日期: 2005-08
    上傳時間: 2017-06-27 17:09:27 (UTC+8)
    摘要: 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}.
    關聯: J.Phys. A:Math. Gen., Vol.38, pp.6271-6276
    資料類型: article
    DOI: 10.1088/0305-4470/38/28/001
    顯示於類別:[應用數學系] 期刊論文

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