STATISTICAL-MECHANICS OF RELATIVISTIC ANYON-LIKE SYSTEMS

To study the manifestation of the Aharonov-Bohm effect in many-body systems we consider the statistical mechanics of the Gross-Neveu model on a ring (1+1 dimensions) and on a cylinder (2+1 dimensions) with a thin solenoid coinciding with the axis. For such systems with a non-trivial magnetic flux (theta) many thermodynamical observables, such as the order parameter, induced current and virial coefficients, display a periodic but non-analytic dependence on theta. In the (2+1)-dimensional case we further find that there is an interval of theta is-an-element-of (1/2, 2/3) (modulo integers) where parity is always spontaneously broken, independent of the circumference of the cylinder. We show that the mean-field character of the phase transitions is preserved to the leading order in 1/N, by verifying the theta-independence of all the critical exponents. The precise nature of the quasi-particle, locally fermion-like and globally anyon-like, is illuminated through the calculation of the equal-time commutator and the decomposition of the propagator into a sum over paths classified by winding numbers.