Stability and anyonic behavior of systems with M-statistics

Starting with the partition function Z for systems with M-statistics, as proposed in Chen et al. (1996)  [1], we calculate from the metric gαη=∂lnZ∂βαβη 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→∞), cases.