The statistical mechanics of an anyon gas in a magnetic field is addressed. An harmonic regulator is used to define a proper thermodynamic limit. When the magnetic field is sufficiently strong, only exact N -anyon groundstates, where anyons occupy the lowest Landau level, contribute to the equation of state. Particular attention is paid to the interval of definition of the statistical parameter α ∈ [−1, 0] where a gap exists. Interestingly enough, one finds that at the critical filling ν = −1/α where the pressure diverges, the external magnetic field is entirely screened by the flux tubes carried by the anyons.

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The 2-dimensional density of states of an electron is studied for a Poissonian random distribution of point vortices carrying α flux in unit of the quantum of flux. It is shown that, for any given density of impurities, there is a transition, when α ≃ 0.3 − 0.4, from an "almost free" density of state -with only a depletion of states at the bottom of the spectrum characterized by a Lifschitz tail-to a Landau density of state with sharp Landau level oscillations. Several evidences and arguments for this transition -numerical and analyticalare presented.

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