Stability and anyonic behavior of systems with -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 g α η = ∂ ln Z ∂ β α β η 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.