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Haldane-Wu statistics and Rogers dilogarithm | | Andrei G. Bytsko
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14 Nov 2002 | | Journal: | Zap.Nauchn.Semin. 291 (2002) 64-77; J.Math.Sci. 125 (2005) 136-143 | | Subject: | Mathematical Physics; Statistical Mechanics | math-ph cond-mat.stat-mech math.MP | | Abstract: | The Haldane-Wu exclusion statistics is considered from the generalized extensive statistics point of view and certain related mathematical aspects are investigated. A series representation for the corresponding generating function is proven. Equivalence of two formulae for the central charge, derived for the Haldane-Wu statistics via the thermodynamic Bethe ansatz, is established. As a corollary, a series representation with a free parameter for the Rogers dilogarithm is found. It is shown that the generating function, the entropy, and the central charge for the Gentile statistics majorize those for the Haldane-Wu statistics (under appropriate choice of parameters). From this, some dilogarithm inequality is derived. | | Source: | arXiv, math-ph/0211026 | | Services: | Forum | Review | PDF | Favorites | |
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