Complex-valued fractional statistics for D-dimensional harmonic oscillators

A system of isotropic harmonic oscillators obeying the Polychronakos fractional statistics with a complex parameter in a space having the dimension D>1 is studied. Temperature dependences of the thermodynamic functions are analyzed in different temperature domains. The nature of the observed phase transitions is clarified. Both numerical and analytical estimates for the critical temperature are made depending on the number of particles, space dimensionality, and statistics parameter. Approximate correspondence with some other fractional statistics types is established.