Multiple Exclusion Statistics: the $k$-mers problem

TL;DR

This paper introduces a new distribution for particles obeying multiple exclusion statistics, extending Haldane's and Wu's models to correlated states, with applications to lattice gases of $k$-mers and validation through simulations.

Contribution

It proposes a novel multiple exclusion statistics distribution that accounts for correlated state exclusion, generalizing existing models and applying it to $k$-mer lattice gases.

Findings

The new distribution recovers Haldane's and Wu's statistics in the non-correlated limit.

Thermodynamics and occupation results match simulations for $k$-mers from 2 to 10.

Multiple exclusion effects become more significant as $k$ increases.

Abstract

A new distribution for systems of particles obeying statistical exclusion of correlated states is presented following the Haldane's state counting. It relies upon a conjecture to deal with the multiple exclusion that takes place when the states available to single particles are spatially correlated and it can be simultaneously excluded by more than one particle. The Haldane's statistics [F. D. M. Haldane, Phys. Rev. Lett. 67, 937 (1991)] and Wu's distribution [Y.-S. Wu, Phys. Rev. Lett. 52, 2103 (1984)] are recovered in the limit of non-correlated states (constant statistical exclusion) of the multiple exclusion statistics. In addition, the exclusion spectrum function $G(n)$ is introduced to account for the dependence of the statistical exclusion on the occupation-number $n$. Results of thermodynamics and state occupation are shown for ideal lattice gases of linear particles of size $k$ ($k$-mers) where multiple exclusion occurs. Remarkable agreement is found with simulations from $k=2$ to $10$ where multiple exclusion dominates as $k$ increases.