Exactness of anyon superconductivity and its finite-temperature behavior

We study anyon systems that obey 1/n fractional statistics for fixed number density ρ and mass m. We prove rigorously that in the high-temperature regime there is no long-range correlation above T∼(2π/ln2)(${\mathrm{ħ}}^2$ρ/m). At zero temperature we study the exactness and the stability of anyon superconductivity in connection with the integer quantized Hall effect. We also study the topological excitations of the anyon systems and show the exact magnetic flux quantization in units of hc/ne. We have found that the anyon systems undergo a Kosterlitz-Thouless transition at T∼(π/2)(${\mathrm{ħ}}^2$ρ/${\mathit{mn}}^2$).