A Generalization of Haldane state-counting procedure and $\pi$-deformations of statistics

TL;DR

This paper generalizes Haldane's exclusion statistics to include all linear deformations, providing new distribution functions and analyzing their thermodynamic properties with potential physical applications.

Contribution

It introduces a comprehensive generalization of Haldane's state-counting and distribution functions for linear exclusion statistics parametrized by symmetric group elements.

Findings

Derived new distribution functions for generalized exclusion statistics.

Analyzed low-temperature thermodynamics of the generalized systems.

Compared results with previous studies on $g$-ons.

Abstract

We consider the generalization of Haldane's state-counting procedure to describe all possible types of exclusion statistics which are linear in the deformation parameter $g$. The statistics are parametrized by elements of the symmetric group of the particles in question. For several specific cases we determine the form of the distribution functions which generalizes results obtained by Wu. Using them we analyze the low-temperature behavior and thermodynamic properties of these systems and compare our results with previous studies of the thermodynamics of a gas of $g$-ons. Various possible physical applications of these constructions are discussed.