Haldane-Wu statistics and Rogers dilogarithm

TL;DR

This paper explores the mathematical properties of Haldane-Wu exclusion statistics, establishing new series representations and inequalities related to the Rogers dilogarithm and central charge calculations.

Contribution

It introduces a series representation for the generating function and a dilogarithm inequality, linking Haldane-Wu and Gentile statistics through mathematical analysis.

Findings

Proven series representation for the generating function.

Established equivalence of two formulas for the central charge.

Derived a dilogarithm inequality from statistical comparisons.

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.