Equation of State of an Anyon Gas in a Strong Magnetic Field

Abstract

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 $α\in[-1,0]$ 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.