Stability and anyonic behavior of systems with M-statistics

TL;DR

This paper investigates the stability and anyonic properties of systems with M-statistics by analyzing the scalar curvature derived from the partition function, revealing how these properties depend on fugacity and maximum occupancy.

Contribution

It provides a detailed analysis of the scalar curvature and stability for M-statistics systems, highlighting their anyonic behavior and comparing with fermionic and bosonic cases.

Findings

Scalar curvature reveals anyonic behavior depending on fugacity and M.

Stability varies with M, showing differences from fermionic and bosonic limits.

Systems with M>1 exhibit unique stability and statistical properties.

Abstract

Starting with the partition function $Z$ for systems with $M$-statistics, as proposed in \cite{WND}, we calculate from the metric $g_{\alpha\eta}=\frac{\partial \ln Z}{\partial\beta^{\alpha}\beta^{\eta}}$ the scalar curvature $R$ in two and three dimensions. Our results exhibit the details of the anyonic behavior as a function of the fugacity $z$ and the identical particle maximum occupancy number $M$. We also compare the stability of systems for $M>1$with the fermionic (M=1), and bosonic ($M\rightarrow \infty$), cases.