ONE-DIMENSIONAL STATISTICAL-MECHANICS FOR IDENTICAL PARTICLES - THE CALOGERO AND ANYON CASES

The thermodynamic of particles with intermediate statistics interpolat ing between Bose and Fermi statistics is addressed in the simple case where there is one quantum number per particle. Such systems are essen tially one-dimensional. As an illustration, one considers the anyon mo del restricted to the lowest Landau level of a strong magnetic field a t low temperature, the generalization of this model to several particl es species, and the one-dimensional Calogero model. One reviews a unif ied algorithm to compute the statistical mechanics of these systems. I t is pointed out that Haldane's generalization of the Pauli's principl e can be deduced from the anyon model in a strong magnetic field at lo w temperature.