Stability and anyonic behavior of systems with M-statistics

Starting with the partition function $Z$ for systems with $M$-statistics, as proposed in \cite{WND}, we calculate from the metric $g_{\alpha \eta }=\frac{\mathrm{\partial }\ln Z}{\mathrm{\partial }{\beta }^{\alpha }{\beta }^{\eta }}$ 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.